diff --git a/CHANGELOG.md b/CHANGELOG.md
index 39c59c4..90f0b08 100644
--- a/CHANGELOG.md
+++ b/CHANGELOG.md
@@ -1,5 +1,6 @@
 ## master (unreleased)
 
+- Fix `add_refernce_concurrently` when adding non polymorphic references
 - Fix progress for background migrations with small number of records
 
 ## 0.19.5 (2024-09-20)
diff --git a/lib/online_migrations/schema_statements.rb b/lib/online_migrations/schema_statements.rb
index 4f9e29c..c63dee3 100644
--- a/lib/online_migrations/schema_statements.rb
+++ b/lib/online_migrations/schema_statements.rb
@@ -655,7 +655,7 @@ def add_reference_concurrently(table_name, ref_name, **options)
         add_column(table_name, column_name, type, null: allow_null)
       end
 
-      if !column_exists?(table_name, type_column_name)
+      if options[:polymorphic] && !column_exists?(table_name, type_column_name)
         allow_null = options[:polymorphic].is_a?(Hash) ? options[:polymorphic][:null] : true
         add_column(table_name, type_column_name, :string, null: allow_null)
       end
diff --git a/test/schema_statements/add_reference_concurrently_test.rb b/test/schema_statements/add_reference_concurrently_test.rb
index 1039f63..add71f6 100644
--- a/test/schema_statements/add_reference_concurrently_test.rb
+++ b/test/schema_statements/add_reference_concurrently_test.rb
@@ -32,6 +32,7 @@ def test_add_reference_concurrently
 
       Milestone.reset_column_information
       assert_includes Milestone.column_names, "project_id"
+      assert_not_includes Milestone.column_names, "project_type"
     end
 
     def test_add_reference_concurrently_adds_index