The performance of a heat pump using $CO_2$ is predicted and analyzed by using a cycle simulation model developed in this study. Cycle simulations are conducted by varying design parameters and operating conditions with the applications of advanced techniques to improve system performance. The applied systems in the simulations are internal heat exchanger, expander, and 2-stage compression with intercooling. As a result, the applications of advanced techniques improve the heating and cooling performances of the transcritical $CO_2$ cycle by 8∼26％ and 20∼30％, respectively, over the basic cycle.