Potential advantages of using vapor injection in a two stage rotary compressor for a $CO_2$ heat pump water heater system were addressed in this paper by numerical simulation. Vapor separated from a flash tank in the middle of the expansion process can be used for injection into the second stage suction plenum of the compressor to improve the system performance. Vapor injection increases the intermediate pressure between the two stages, thus increasing the first stage compressor work and reducing that of the second stage. As a whole, however, the compressor input power increases due to injected mass flow rate for the second stage. Computer simulation showed that increment of the cooling capacity by vapor injection exceeded that of the compressor work, thus improving the system performance. COP improvement by vapor injection was calculated to be about 5-14% for normal operating conditions. With vapor injection, a maximum COP was found when the displacement volume of the second stage becomes 90-95% of that of the first stage of the compressor.