diff --git a/CHANGELOG.md b/CHANGELOG.md
index 9330b1e7fdfae..0ecc4a81a307b 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -345,6 +345,9 @@ The format is based on [Keep a Changelog](http://keepachangelog.com/en/1.0.0/).
 
 - Fixed a bug where calling `log` with a `Metric` instance would raise an error if it was a nested attribute of the model ([#8181](https://github.com/PyTorchLightning/pytorch-lightning/pull/8181))
 
+
+- Fixed a bug where using `precision=64` would cause buffers with complex dtype to be cast to real ([#8208](https://github.com/PyTorchLightning/pytorch-lightning/pull/8208))
+
 ## [1.3.7] - 2021-06-22
 
 - Fixed a bug where skipping an optimizer while using amp causes amp to trigger an assertion error ([#7975](https://github.com/PyTorchLightning/pytorch-lightning/pull/7975))
diff --git a/pytorch_lightning/plugins/precision/double.py b/pytorch_lightning/plugins/precision/double.py
index 86177c5500e2f..064c65b500f29 100644
--- a/pytorch_lightning/plugins/precision/double.py
+++ b/pytorch_lightning/plugins/precision/double.py
@@ -96,7 +96,7 @@ def connect(
         incoming floating point data to double (``torch.float64``) precision. Does not alter `optimizers` or
         `lr_schedulers`.
         """
-        model = cast(pl.LightningModule, model.to(dtype=torch.float64))
+        model = cast(pl.LightningModule, model.double())
         model = LightningDoublePrecisionModule(model)
 
         return super().connect(model, optimizers, lr_schedulers)
diff --git a/tests/plugins/test_double_plugin.py b/tests/plugins/test_double_plugin.py
index be4f690f25ed6..302ee985b2379 100644
--- a/tests/plugins/test_double_plugin.py
+++ b/tests/plugins/test_double_plugin.py
@@ -20,6 +20,7 @@
 
 from pytorch_lightning import Trainer
 from pytorch_lightning.plugins import DoublePrecisionPlugin
+from pytorch_lightning.utilities import _TORCH_GREATER_EQUAL_1_7
 from tests.helpers.boring_model import BoringModel, RandomDataset
 from tests.helpers.runif import RunIf
 
@@ -123,7 +124,28 @@ def predict_dataloader(self):
         return DataLoader(RandomDataset(32, 64))
 
 
-@pytest.mark.parametrize('boring_model', (DoublePrecisionBoringModel, DoublePrecisionBoringModelNoForward))
+class DoublePrecisionBoringModelComplexBuffer(BoringModel):
+
+    def __init__(self):
+        super().__init__()
+
+        self.register_buffer("complex_buffer", torch.complex(torch.rand(10), torch.rand(10)), False)
+
+    def on_fit_start(self):
+        assert self.layer.weight.dtype == torch.float64
+        assert self.complex_buffer.dtype == torch.complex64
+
+
+@pytest.mark.parametrize(
+    'boring_model', [
+        DoublePrecisionBoringModel,
+        DoublePrecisionBoringModelNoForward,
+        pytest.param(
+            DoublePrecisionBoringModelComplexBuffer,
+            marks=pytest.mark.skipif(not _TORCH_GREATER_EQUAL_1_7, reason="torch.complex not available")
+        ),
+    ]
+)
 def test_double_precision(tmpdir, boring_model):
     model = boring_model()