As the global warming becomes a serious environmental problem, studies of reducing $CO_2$ emission in power generation area are in progress all over the world. One of the carbon capture and storage(CCS) technologies is known as oxy-fuel combustion power generation system. In the oxy-fuel combustion system, the exhaust gas is mainly composed of $CO_2$ and $H_2O$. Thus, high-purity $CO_2$ can be obtained after a proper $H_2O$ removal process. In this paper, an oxy-fuel combustion cycle that recovers the waste heat of a high-temperature fuel cell is analyzed thermodynamically. Variations of characteristics of $CO_2$ and $H_2O$ mixture which is extracted from the condenser and power consumption required to obtain highly-pure $CO_2$ gas were examined according to the variation of the condensing pressure. The influence of the number of compression stages on the power consumption of the $CO_2$ capture process was analyzed, and the overall system performance was also investigated.