The performance of a residential heating and cooling system with $CO_2$ is predicted by using a cycle simulation model. The simulations are conducted by varying design parameters and operating conditions. The efficiency of the transcritical cycle can be improved by utilizing the advantages in heat transfer characteristics of $CO_2$ and developing microchannel indoor and outdoor heat exchangers. For the designed system of this study, the predicted COP of the heat pump system is approximately 3.5 in the heating mode and 3.0 in the cooling mode. The predicted optimal discharge pressure for the heat pump system is approximately 11 MPa in the heating mode and 9 MPa in the cooling mode.