diff --git a/CHANGELOG.md b/CHANGELOG.md
index e0afbb8badbbb..493466ac5ad1a 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -191,6 +191,8 @@ 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))
+
 
 ## [1.4.0] - 2021-07-27
 
diff --git a/pytorch_lightning/tuner/batch_size_scaling.py b/pytorch_lightning/tuner/batch_size_scaling.py
index 1eda93cd831b3..c048ce0a42dd9 100644
--- a/pytorch_lightning/tuner/batch_size_scaling.py
+++ b/pytorch_lightning/tuner/batch_size_scaling.py
@@ -174,6 +174,7 @@ def _run_binsearch_scaling(
     """Batch scaling mode where the size is initially is doubled at each iteration
     until an OOM error is encountered. Hereafter, the batch size is further
     refined using a binary search"""
+    low = 1
     high = None
     count = 0
     while True: