diff --git a/global-requirements.txt b/global-requirements.txt
index 7ed6c2c9eb..922428a960 100644
--- a/global-requirements.txt
+++ b/global-requirements.txt
@@ -185,7 +185,8 @@ oslo.rootwrap  # Apache-2.0
 oslo.serialization!=2.19.1,<3.0.0;python_version<'3.0'  # Apache-2.0
 oslo.serialization!=2.19.1;python_version>='3.0'  # Apache-2.0
 oslo.service!=1.28.1  # Apache-2.0
-oslo.upgradecheck  # Apache-2.0
+oslo.upgradecheck<0.4.0;python_version=='2.7'  # Apache-2.0
+oslo.upgradecheck;python_version>='3.6'  # Apache-2.0
 # NOTE(lajoskatona): oslo.utils version between 3.39.1 and 3.40.1 excluded due to bug 1812922
 oslo.utils!=3.39.1,!=3.40.0,!=3.40.1,<4.0.0;python_version<'3.0'  # Apache-2.0
 oslo.utils!=3.39.1,!=3.40.0,!=3.40.1;python_version>='3.0'  # Apache-2.0
diff --git a/upper-constraints.txt b/upper-constraints.txt
index c9227bec68..c9ec582049 100644
--- a/upper-constraints.txt
+++ b/upper-constraints.txt
@@ -542,7 +542,9 @@ tricircleclient===0.6.0
 WSME===0.9.3
 proboscis===1.2.6.0
 fortiosclient===0.0.3
-oslo.upgradecheck===0.3.2
+oslo.upgradecheck===0.3.2;python_version=='2.7'
+oslo.upgradecheck===0.4.0;python_version=='3.6'
+oslo.upgradecheck===0.4.0;python_version=='3.7'
 stevedore===1.32.0
 botocore===1.14.13
 xmltodict===0.12.0