The design of a cold atom clock in space (CACS) and its recent progress are described. The CACS is a high precision cold Rubidium atom clock for the application in microgravity environment, which has four parts, including physics, laser source, microwave source, and control system. The first CACS clock science run has been achieved as described. The essential operations of a space cold atom rubidium clock have been demonstrated in the prototype system. The key results of a clock including the ultrahigh vacuum degree, the atomic temperature， and the linewidth of the Ramsey fringes, satisfy the demands of a space cold atom clock. Based on this prototype, an engineering model for space application has been under development.