diff --git a/airflow/providers/google/cloud/transfers/gcs_to_gcs.py b/airflow/providers/google/cloud/transfers/gcs_to_gcs.py
index a3d6db8636..70b6288e72 100644
--- a/airflow/providers/google/cloud/transfers/gcs_to_gcs.py
+++ b/airflow/providers/google/cloud/transfers/gcs_to_gcs.py
@@ -69,6 +69,8 @@ class GCSToGCSOperator(BaseOperator):
         of copied to the new location. This is the equivalent of a mv command
         as opposed to a cp command.
     :type move_object: bool
+    :param replace: Whether you want to replace existing destination files or not.
+    :type replace: bool
     :param delimiter: This is used to restrict the result to only the 'files' in a given 'folder'.
         If source_objects = ['foo/bah/'] and delimiter = '.avro', then only the 'files' in the
         folder 'foo/bah/' with '.avro' delimiter will be copied to the destination object.
@@ -176,6 +178,7 @@ class GCSToGCSOperator(BaseOperator):
                  destination_object=None,
                  delimiter=None,
                  move_object=False,
+                 replace=True,
                  gcp_conn_id='google_cloud_default',
                  google_cloud_storage_conn_id=None,
                  delegate_to=None,
@@ -198,6 +201,7 @@ class GCSToGCSOperator(BaseOperator):
         self.destination_object = destination_object
         self.delimiter = delimiter
         self.move_object = move_object
+        self.replace = replace
         self.gcp_conn_id = gcp_conn_id
         self.delegate_to = delegate_to
         self.last_modified_time = last_modified_time
@@ -276,6 +280,21 @@ class GCSToGCSOperator(BaseOperator):
         self.log.info('Delimiter ignored because wildcard is in prefix')
         prefix_, delimiter = prefix.split(WILDCARD, 1)
         objects = hook.list(self.source_bucket, prefix=prefix_, delimiter=delimiter)
+        if not self.replace:
+            # If we are not replacing, list all files in the Destination GCS bucket
+            # and only keep those files which are present in
+            # Source GCS bucket and not in Destination GCS bucket
+
+            existing_objects = hook.list(self.destination_bucket, prefix=prefix_, delimiter=delimiter)
+
+            objects = set(objects) - set(existing_objects)
+            if len(objects) > 0:
+                self.log.info(
+                    '%s files are going to be synced: %s.', len(objects), objects
+                )
+            else:
+                self.log.info(
+                    'There are no new files to sync. Have a nice day!')
         for source_object in objects:
             if self.destination_object is None:
                 destination_object = source_object
diff --git a/tests/providers/google/cloud/transfers/test_gcs_to_gcs.py b/tests/providers/google/cloud/transfers/test_gcs_to_gcs.py
index 49c067b6ae..a51b101147 100644
--- a/tests/providers/google/cloud/transfers/test_gcs_to_gcs.py
+++ b/tests/providers/google/cloud/transfers/test_gcs_to_gcs.py
@@ -86,6 +86,21 @@ class TestGoogleCloudStorageToCloudStorageOperator(unittest.TestCase):
             TEST_BUCKET, prefix="test_object", delimiter=""
         )
 
+    @mock.patch('airflow.providers.google.cloud.transfers.gcs_to_gcs.GCSHook')
+    def test_execute_wildcard_with_replace_flag_false(self, mock_hook):
+        operator = GCSToGCSOperator(
+            task_id=TASK_ID, source_bucket=TEST_BUCKET,
+            source_object=SOURCE_OBJECT_WILDCARD_SUFFIX,
+            destination_bucket=DESTINATION_BUCKET,
+            replace=False)
+
+        operator.execute(None)
+        mock_calls = [
+            mock.call(TEST_BUCKET, prefix="test_object", delimiter=""),
+            mock.call(DESTINATION_BUCKET, prefix="test_object", delimiter=""),
+        ]
+        mock_hook.return_value.list.assert_has_calls(mock_calls)
+
     @mock.patch('airflow.providers.google.cloud.transfers.gcs_to_gcs.GCSHook')
     def test_execute_prefix_and_suffix(self, mock_hook):
         operator = GCSToGCSOperator(