diff --git a/tests/callbacks/test_early_stopping.py b/tests/callbacks/test_early_stopping.py
index abe21b9d28..b7711e8aae 100644
--- a/tests/callbacks/test_early_stopping.py
+++ b/tests/callbacks/test_early_stopping.py
@@ -13,15 +13,17 @@
 # limitations under the License.
 import os
 import pickle
-from unittest import mock
 
 import cloudpickle
+import numpy as np
 import pytest
 import torch
+from unittest import mock
 
+from pytorch_lightning import _logger
 from pytorch_lightning import Trainer, seed_everything
 from pytorch_lightning.callbacks import EarlyStopping, ModelCheckpoint
-from tests.base import EvalModelTemplate
+from tests.base import EvalModelTemplate, BoringModel
 from pytorch_lightning.utilities.exceptions import MisconfigurationException
 
 
@@ -204,3 +206,92 @@ def test_early_stopping_functionality_arbitrary_key(tmpdir):
     )
     trainer.fit(model)
     assert trainer.current_epoch >= 5, 'early_stopping failed'
+
+
+@pytest.mark.parametrize('step_freeze, min_steps, min_epochs',[(5, 1, 1), (5, 1, 3), (3, 15, 1)])
+def test_min_steps_override_early_stopping_functionality(tmpdir, step_freeze, min_steps, min_epochs):
+    """Excepted Behaviour:
+    IF `min_steps` was set to a higher value than the `trainer.global_step` when `early_stopping` is being triggered,
+    THEN the trainer should continue until reaching `trainer.global_step` == `min_steps`, and stop.
+
+    IF `min_epochs` resulted in a higher number of steps than the `trainer.global_step` when `early_stopping` is being triggered,
+    THEN the trainer should continue until reaching `trainer.global_step` == `min_epochs * len(train_dataloader)`, and stop.
+    This test validate this expected behaviour
+
+    IF both `min_epochs` and `min_steps` are provided and higher than the `trainer.global_step` when `early_stopping` is being triggered,
+    THEN the highest between `min_epochs * len(train_dataloader)` and `min_steps` would be reached.
+
+    Caviat: IF min_steps is divisible by len(train_dataloader), then it will do min_steps + len(train_dataloader)
+
+    This test validate those expected behaviours
+    """
+
+    _logger.disabled = True
+
+    original_loss_value = 10
+    limit_train_batches = 3
+    patience = 3
+
+    class Model(BoringModel):
+
+        def __init__(self, step_freeze):
+            super(Model, self).__init__()
+
+            self._step_freeze = step_freeze
+
+            self._loss_value = 10.0
+            self._eps = 1e-1
+            self._count_decrease = 0
+            self._values = []
+
+        def training_step(self, batch, batch_idx):
+            output = self.layer(batch)
+            loss = self.loss(batch, output)
+            return {"loss": loss}
+
+        def validation_step(self, batch, batch_idx):
+            return {"test_val_loss": self._loss_value}
+
+        def validation_epoch_end(self, outputs):
+            _mean = np.mean([x['test_val_loss'] for x in outputs])
+            if self.trainer.global_step <= self._step_freeze:
+                self._count_decrease += 1
+                self._loss_value -= self._eps
+            self._values.append(_mean)
+            return {"test_val_loss": _mean}
+
+    model = Model(step_freeze)
+    model.training_step_end = None
+    model.test_dataloader = None
+    early_stop_callback = EarlyStopping(monitor="test_val_loss", patience=patience, verbose=True)
+    trainer = Trainer(
+        default_root_dir=tmpdir,
+        callbacks=[early_stop_callback],
+        limit_train_batches=limit_train_batches,
+        limit_val_batches=2,
+        min_steps=min_steps,
+        min_epochs=min_epochs
+    )
+    trainer.fit(model)
+
+    # Make sure loss was properly decreased
+    assert abs(original_loss_value - (model._count_decrease) * model._eps - model._loss_value) < 1e-6
+
+    pos_diff = (np.diff(model._values) == 0).nonzero()[0][0]
+
+    # Compute when the latest validation epoch end happened
+    latest_validation_epoch_end = (pos_diff // limit_train_batches) * limit_train_batches
+    if pos_diff % limit_train_batches == 0:
+        latest_validation_epoch_end += limit_train_batches
+
+    # Compute early stopping latest step
+    by_early_stopping = latest_validation_epoch_end + (1 + limit_train_batches) * patience
+
+    # Compute min_epochs latest step
+    by_min_epochs = min_epochs * limit_train_batches
+
+    # Make sure the trainer stops for the max of all minimun requirements
+    assert trainer.global_step == max(min_steps, by_early_stopping, by_min_epochs), \
+        (trainer.global_step, max(min_steps, by_early_stopping, by_min_epochs), step_freeze, min_steps, min_epochs)
+
+    _logger.disabled = False