diff --git a/lower-constraints.txt b/lower-constraints.txt
index 9cb8be55..1cddf2fa 100644
--- a/lower-constraints.txt
+++ b/lower-constraints.txt
@@ -14,7 +14,7 @@ oslo.service==1.31.0
 oslo.utils==4.4.0
 oslotest==3.2.0
 pbr==4.0.0
-pyOpenSSL==19.1.0
+pyOpenSSL==20.0.0
 python-subunit==1.0.0
 requests-mock==1.2.0
 sphinx==2.0.0
diff --git a/requirements.txt b/requirements.txt
index cf19f83f..2b685539 100644
--- a/requirements.txt
+++ b/requirements.txt
@@ -13,4 +13,4 @@ oslo.log>=4.2.1 # Apache-2.0
 oslo.serialization>=2.28.1 # Apache-2.0
 oslo.service>=1.31.0 # Apache-2.0
 oslo.utils>=4.4.0 # Apache-2.0
-pyOpenSSL>=19.1.0 # Apache-2.0
+pyOpenSSL>=20.0.0 # Apache-2.0