A cold storage heat exchanger includes multiple refrigerant tubes arranged to provide a clearance therebetween, multiple cold storage containers each of which is interposed between adjacent refrigerant tubes, bonded to the adjacent refrigerant tubes and defining a compartment receiving a cold storage material. A surface of each cold storage container has multiple protrusion portions, and each protrusion portion protrudes outward and is in contact with the adjacent refrigerant tubes. The multiple protrusion portions are arranged in a zigzag manner or extend continuously in an air flow direction.