diff --git a/packages/google-cloud-python-speech/setup.py b/packages/google-cloud-python-speech/setup.py
index 60f53f57a5e4..52cb3ccd0c1c 100644
--- a/packages/google-cloud-python-speech/setup.py
+++ b/packages/google-cloud-python-speech/setup.py
@@ -29,7 +29,7 @@
 # 'Development Status :: 5 - Production/Stable'
 release_status = 'Development Status :: 4 - Beta'
 dependencies = [
-    'google-api-core[grpc]<2.0.0dev,>=0.1.4',
+    'google-api-core[grpc] >= 1.4.1, < 2.0.0dev',
 ]
 extras = {
 }