diff --git a/sdk/core/azure-core/HISTORY.md b/sdk/core/azure-core/HISTORY.md
index 7aef0dc79e86..e0b8f4be866d 100644
--- a/sdk/core/azure-core/HISTORY.md
+++ b/sdk/core/azure-core/HISTORY.md
@@ -7,6 +7,7 @@
 
 - Fixed a bug that sends None as request_id #9545
 - Enable mypy for customers #9572
+- Handle TypeError in deep copy #9620
 
 ## 1.2.1 (2020-01-14)
 
diff --git a/sdk/core/azure-core/azure/core/pipeline/transport/_base.py b/sdk/core/azure-core/azure/core/pipeline/transport/_base.py
index b9c416211f2d..82dc54fd4cc9 100644
--- a/sdk/core/azure-core/azure/core/pipeline/transport/_base.py
+++ b/sdk/core/azure-core/azure/core/pipeline/transport/_base.py
@@ -226,7 +226,7 @@ def __deepcopy__(self, memo=None):
             data = copy.deepcopy(self.body, memo)
             files = copy.deepcopy(self.files, memo)
             return HttpRequest(self.method, self.url, self.headers, files, data)
-        except ValueError:
+        except (ValueError, TypeError):
             return copy.copy(self)
 
     @property
diff --git a/sdk/core/azure-core/tests/test_universal_pipeline.py b/sdk/core/azure-core/tests/test_universal_pipeline.py
index 0093bef899b1..c82892ecd476 100644
--- a/sdk/core/azure-core/tests/test_universal_pipeline.py
+++ b/sdk/core/azure-core/tests/test_universal_pipeline.py
@@ -69,6 +69,19 @@ def __deepcopy__(self, memodict={}):
     assert request_history.http_request.url == request.url
     assert request_history.http_request.method == request.method
 
+def test_request_history_type_error():
+    class Non_deep_copiable(object):
+        def __deepcopy__(self, memodict={}):
+            raise TypeError()
+
+    body = Non_deep_copiable()
+    request = HttpRequest('GET', 'http://127.0.0.1/', {'user-agent': 'test_request_history'})
+    request.body = body
+    request_history = RequestHistory(request)
+    assert request_history.http_request.headers == request.headers
+    assert request_history.http_request.url == request.url
+    assert request_history.http_request.method == request.method
+
 @mock.patch('azure.core.pipeline.policies._universal._LOGGER')
 def test_no_log(mock_http_logger):
     universal_request = HttpRequest('GET', 'http://127.0.0.1/')