A cold storage heat exchanger has refrigerant pipes fins, and cold-storage-medium containers. The cold-storage-medium container is arranged next to the refrigerant pipe. A cold storage medium is accommodated in the cold-storage-medium container in order to leave an air cell, and to provide a filling ratio of less than 90%. The cold-storage-medium container has a plurality of depressions at an inside of the cold-storage-medium container. The depression is a dimple. The plurality of depressions are joined each other at top parts and provide high rigidity. The cold-storage-medium container is positioned on the refrigerant pipe by an engaging projection. An open end of an open depression is covered by the refrigerant pipe. The cold storage medium can flow into the open depression. Therefore, the cold storage medium may directly contact the refrigerant pipe, and is directly cooled with the refrigerant.