diff --git a/Lib/fontTools/varLib/__init__.py b/Lib/fontTools/varLib/__init__.py
index 2e87545d3..0320ef073 100644
--- a/Lib/fontTools/varLib/__init__.py
+++ b/Lib/fontTools/varLib/__init__.py
@@ -232,6 +232,11 @@ def _add_avar(font, axes, mappings, axisTags):
             for mapping in mappings
         ]
 
+        # If base-master is missing, insert it at zero location.
+        if not any(all(v == 0 for k, v in loc.items()) for loc in inputLocations):
+            inputLocations.insert(0, {})
+            outputLocations.insert(0, {})
+
         model = models.VariationModel(inputLocations, axisTags)
         builder = varStore.OnlineVarStoreBuilder(axisTags)
         builder.setModel(model)
diff --git a/Tests/varLib/data/BuildAvar2.designspace b/Tests/varLib/data/BuildAvar2.designspace
index 0a22fe6aa..1cfa94ab3 100644
--- a/Tests/varLib/data/BuildAvar2.designspace
+++ b/Tests/varLib/data/BuildAvar2.designspace
@@ -14,13 +14,6 @@
             <labelname xml:lang="en">Weight</labelname>
         </axis>
         <mappings>
-            <mapping>
-                <input>
-                    <dimension name="weight" xvalue="90"/>
-                </input>
-                <output>
-                </output>
-            </mapping>
             <mapping>
                 <input>
                     <dimension name="weight" xvalue="128"/>