Relatively low cycle performance of a conventional $CO_2$ system is partly due to significant increase in friction loss in the expansion process, since the pressure drop across the expansion device is considerably large compared to a conventional refrigeration cycle. To recover friction loss and increase refrigeration effect by providing isentropic expansion, a rotary vane type expander has been designed. Performance of the designed expander has been investigated by numerical simulation. With the pressure condition of 9 MPa/4.5 MPa and inlet temperature of $35^{circ}C$, volumetric, isentropic, and mechanical efficiencies of the expander are calculated to be 58.1%, 101.1%, and 78.8%, respectively, resulting in total expander efficiency of 46.3%. With this expander, COP of a $CO_2$ refrigeration cycle is estimated to be improved by about 14%.