diff --git a/CHANGELOG.md b/CHANGELOG.md
index 35404e85a5816..57e717a91b017 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -203,9 +203,13 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/en/1.0.0/).
 
 - Fixed bug where data-loading functions where not getting the correct running stage passed ([#8858](https://github.com/PyTorchLightning/pytorch-lightning/pull/8858))
 
+
 - Fixed a bug in the binary search mode of auto batch size scaling where exception was thrown if the first trainer run resulted in OOM ([#8954](https://github.com/PyTorchLightning/pytorch-lightning/pull/8954))
 
 
+- Fixed not setting a default value for `max_epochs` if `max_time` was specified on the `Trainer` constructor ([#9072](https://github.com/PyTorchLightning/pytorch-lightning/pull/9072))
+
+
 ## [1.4.3] - 2021-08-17
 
 - Fixed plateau scheduler stepping on incomplete epoch ([#8861](https://github.com/PyTorchLightning/pytorch-lightning/pull/8861))
diff --git a/pytorch_lightning/trainer/trainer.py b/pytorch_lightning/trainer/trainer.py
index 739e34aa249b5..c80c368aaad4e 100644
--- a/pytorch_lightning/trainer/trainer.py
+++ b/pytorch_lightning/trainer/trainer.py
@@ -378,8 +378,8 @@ def __init__(
         self.tuner = Tuner(self)
 
         fit_loop = FitLoop(
-            min_epochs=(1 if (min_epochs is None and min_steps is None) else min_epochs),
-            max_epochs=(1000 if (max_epochs is None and max_steps is None) else max_epochs),
+            min_epochs=(1 if (min_epochs is None and min_steps is None and max_time is None) else min_epochs),
+            max_epochs=(1000 if (max_epochs is None and max_steps is None and max_time is None) else max_epochs),
         )
         training_epoch_loop = TrainingEpochLoop(min_steps, max_steps)
         training_batch_loop = TrainingBatchLoop()
diff --git a/tests/callbacks/test_timer.py b/tests/callbacks/test_timer.py
index 44d3c305bb1ac..c7b636d3f843a 100644
--- a/tests/callbacks/test_timer.py
+++ b/tests/callbacks/test_timer.py
@@ -42,6 +42,11 @@ def on_fit_start(self):
         trainer.fit(TestModel())
     assert "callbacks list already contains a Timer" in caplog.text
 
+    seconds = 1
+    trainer = Trainer(max_time=dict(seconds=seconds))
+    assert trainer.max_epochs is None
+    assert trainer.max_steps is None
+
 
 @pytest.mark.parametrize(
     "duration,expected",