The $CO_{2}$ refrigeration cycle is expected to reduce the compressor work and increase the COP by applying two-phase ejector as a device for the recovery of dissipated expansion energy. In this study, the performance of the cycle was simulated and effects of the ejector shapes on the performance of the $CO_{2}$ refrigeration cycle were investigated. The following results were obtained through the cycle simulation. The COP of the $CO_{2}$ refrigeration cycle with two-phase ejector flow which expansion is occured in the isentropic manner is increased by a maximum of 24 $\%$ than the basic cycle with expansion valve If the velocity nonequilibrium in the mixing process is assumed the COP of the cycle is increased with the increase of the length and the decrease of the section area of the mixing tube. The best cycle performance is obtained when the divergent angle of diffuser is 7.