diff --git a/docs/source/en/trainer.md b/docs/source/en/trainer.md
index 916ae6428e..37d8baf3d7 100644
--- a/docs/source/en/trainer.md
+++ b/docs/source/en/trainer.md
@@ -432,6 +432,57 @@ trainer = trl.SFTTrainer(
 trainer.train()
 ```
 
+## GrokAdamW optimizer
+
+The GrokAdamW optimizer is designed to enhance training performance and stability, particularly for models that benefit from grokking signal functions. To use GrokAdamW, first install the optimizer package with `pip install grokadamw`.
+
+<Tip>
+
+GrokAdamW is particularly useful for models that require advanced optimization techniques to achieve better performance and stability.
+
+</Tip>
+
+Below is a simple script to demonstrate how to fine-tune [google/gemma-2b](https://huggingface.co/google/gemma-2b) on the IMDB dataset using the GrokAdamW optimizer:
+
+```python
+import torch
+import datasets
+from transformers import TrainingArguments, AutoTokenizer, AutoModelForCausalLM, Trainer
+
+# Load the IMDB dataset
+train_dataset = datasets.load_dataset('imdb', split='train')
+
+# Define the training arguments
+args = TrainingArguments(
+    output_dir="./test-grokadamw",
+    max_steps=1000,
+    per_device_train_batch_size=4,
+    optim="grokadamw",
+    logging_strategy="steps",
+    logging_steps=1,
+    learning_rate=2e-5,
+    save_strategy="no",
+    run_name="grokadamw-imdb",
+)
+
+# Load the model and tokenizer
+model_id = "google/gemma-2b"
+tokenizer = AutoTokenizer.from_pretrained(model_id)
+model = AutoModelForCausalLM.from_pretrained(model_id, low_cpu_mem_usage=True).to(0)
+
+# Initialize the Trainer
+trainer = Trainer(
+    model=model,
+    args=args,
+    train_dataset=train_dataset,
+)
+
+# Train the model
+trainer.train()
+```
+
+This script demonstrates how to fine-tune the `google/gemma-2b` model on the IMDB dataset using the GrokAdamW optimizer. The `TrainingArguments` are configured to use GrokAdamW, and the dataset is passed to the `Trainer` for training.
+
 ## Accelerate and Trainer
 
 The [`Trainer`] class is powered by [Accelerate](https://hf.co/docs/accelerate), a library for easily training PyTorch models in distributed environments with support for integrations such as [FullyShardedDataParallel (FSDP)](https://pytorch.org/blog/introducing-pytorch-fully-sharded-data-parallel-api/) and [DeepSpeed](https://www.deepspeed.ai/).
diff --git a/src/transformers/testing_utils.py b/src/transformers/testing_utils.py
index 608e278ecf..6b04ed7426 100644
--- a/src/transformers/testing_utils.py
+++ b/src/transformers/testing_utils.py
@@ -76,6 +76,7 @@ from .utils import (
     is_g2p_en_available,
     is_galore_torch_available,
     is_gguf_available,
+    is_grokadamw_available,
     is_ipex_available,
     is_jieba_available,
     is_jinja_available,
@@ -358,6 +359,13 @@ def require_lomo(test_case):
     return unittest.skipUnless(is_lomo_available(), "test requires LOMO")(test_case)
 
 
+def require_grokadamw(test_case):
+    """
+    Decorator marking a test that requires GrokAdamW. These tests are skipped when GrokAdamW isn't installed.
+    """
+    return unittest.skipUnless(is_grokadamw_available(), "test requires GrokAdamW")(test_case)
+
+
 def require_cv2(test_case):
     """
     Decorator marking a test that requires OpenCV.
diff --git a/src/transformers/trainer.py b/src/transformers/trainer.py
index e74b463e8d..094f058469 100755
--- a/src/transformers/trainer.py
+++ b/src/transformers/trainer.py
@@ -153,6 +153,7 @@ from .utils import (
     is_bitsandbytes_available,
     is_datasets_available,
     is_galore_torch_available,
+    is_grokadamw_available,
     is_in_notebook,
     is_ipex_available,
     is_lomo_available,
@@ -1442,6 +1443,23 @@ class Trainer:
                 optimizer_cls = Lomo
 
             optimizer_kwargs.update({"model": model})
+        elif args.optim == OptimizerNames.GROKADAMW:
+            if not is_grokadamw_available():
+                raise ValueError("Please install grokadamw with `pip install grokadamw`")
+
+            from grokadamw import GrokAdamW
+
+            optimizer_cls = GrokAdamW
+            optimizer_kwargs.update(
+                {
+                    "alpha_init": float(optim_args.get("alpha_init", 0.98)),
+                    "lamb": float(optim_args.get("lamb", 2.0)),
+                    "gamma": float(optim_args.get("gamma", 0.1)),
+                    "grokking_signal_decay_rate": float(optim_args.get("grokking_signal_decay_rate", 0.1)),
+                    "gradient_clipping": float(optim_args.get("gradient_clipping", 1.0)),
+                }
+            )
+
         else:
             raise ValueError(f"Trainer cannot instantiate unsupported optimizer: {args.optim}")
         return optimizer_cls, optimizer_kwargs
diff --git a/src/transformers/training_args.py b/src/transformers/training_args.py
index 57605fd945..1058b8356b 100644
--- a/src/transformers/training_args.py
+++ b/src/transformers/training_args.py
@@ -175,6 +175,7 @@ class OptimizerNames(ExplicitEnum):
     GALORE_ADAFACTOR_LAYERWISE = "galore_adafactor_layerwise"
     LOMO = "lomo"
     ADALOMO = "adalomo"
+    GROKADAMW = "grokadamw"
 
 
 # Sometimes users will pass in a `str` repr of a dict in the CLI
diff --git a/src/transformers/utils/__init__.py b/src/transformers/utils/__init__.py
index efe473a6cd..a8aa670c07 100755
--- a/src/transformers/utils/__init__.py
+++ b/src/transformers/utils/__init__.py
@@ -137,6 +137,7 @@ from .import_utils import (
     is_g2p_en_available,
     is_galore_torch_available,
     is_gguf_available,
+    is_grokadamw_available,
     is_hqq_available,
     is_in_notebook,
     is_ipex_available,
diff --git a/src/transformers/utils/import_utils.py b/src/transformers/utils/import_utils.py
index b9936a038a..97d3a5501b 100755
--- a/src/transformers/utils/import_utils.py
+++ b/src/transformers/utils/import_utils.py
@@ -101,6 +101,7 @@ _eetq_available = _is_package_available("eetq")
 _fbgemm_gpu_available = _is_package_available("fbgemm_gpu")
 _galore_torch_available = _is_package_available("galore_torch")
 _lomo_available = _is_package_available("lomo_optim")
+_grokadamw_available = _is_package_available("grokadamw")
 # `importlib.metadata.version` doesn't work with `bs4` but `beautifulsoup4`. For `importlib.util.find_spec`, reversed.
 _bs4_available = importlib.util.find_spec("bs4") is not None
 _coloredlogs_available = _is_package_available("coloredlogs")
@@ -353,6 +354,10 @@ def is_lomo_available():
     return _lomo_available
 
 
+def is_grokadamw_available():
+    return _grokadamw_available
+
+
 def is_pyctcdecode_available():
     return _pyctcdecode_available
 
diff --git a/tests/trainer/test_trainer.py b/tests/trainer/test_trainer.py
index 7378a597c3..ca133a277c 100644
--- a/tests/trainer/test_trainer.py
+++ b/tests/trainer/test_trainer.py
@@ -62,6 +62,7 @@ from transformers.testing_utils import (
     require_bitsandbytes,
     require_deepspeed,
     require_galore_torch,
+    require_grokadamw,
     require_intel_extension_for_pytorch,
     require_lomo,
     require_optuna,
@@ -1366,6 +1367,28 @@ class TrainerIntegrationTest(TestCasePlus, TrainerIntegrationCommon):
             # Check this works
             _ = trainer.train()
 
+    @require_grokadamw
+    @require_torch_gpu
+    def test_grokadamw():
+        config = LlamaConfig(vocab_size=100, hidden_size=32, num_hidden_layers=3, num_attention_heads=4)
+        tiny_llama = LlamaForCausalLM(config)
+        x = torch.randint(0, 100, (128,))
+        train_dataset = RepeatDataset(x)
+
+        with tempfile.TemporaryDirectory() as tmpdir:
+            # Trainer without inf/nan filter
+            args = TrainingArguments(
+                tmpdir,
+                learning_rate=2e-5,
+                logging_steps=5,
+                optim="grokadamw",
+                max_steps=20,
+            )
+            trainer = Trainer(tiny_llama, args, train_dataset=train_dataset)
+
+            # Check this works
+            _ = trainer.train()
+
     def test_galore_matched_modules(self):
         regex_patterns = [r".*.attn.*", r".*.mlp.*"]