A cold storage heat exchanger includes multiple refrigerant tubes, a cold storage container that is bonded to the refrigerant tube and defines a compartment receiving a cold storage material, and an inner fin arranged inside of the cold storage container. The cold storage container has a portion that stops and fixes the inner fin, and the cold storage container has a space where air is sealed. The space of the cold storage container is located at an upper side of the member that stops and fixes the inner fin. Accordingly, a stress applied to the cold storage container in the expansion of the cold storage material can be reduced.