In order to evaluate the performance of carbon dioxide cycle, a simulation model was developed to predict the steady state performance of $CO_2$ transcritical cycle. The expansion process is treated as an isenthalpic throttling process or isentropic expansion process. The mathematical model is based entirely on the basic energy conservation law and thermodynamic and transport properties of $CO_2$. A Parametric study has been conducted in order to investigate the effect of isentropic efficiency of expansion turbine and various operating conditions on the cycle performance. An optimal heat rejection pressure existed for the given evaporating temperature and outlet temperature of gas cooler.