In this study, a performance of steam compression of the centrifugal compressor was analysed. Initially, the performance of the impeller with the vaneless diffuser was investigated by an one-dimensional integral method and a differential method using a CFD(Computational Fluid Dynamics) analysis. The one-dimensional integral method calculated the approximate results without time consuming in comparison with the CFD method. After obtaining the whole modeling of the impeller, diffuser and volute, the CFD analysis was performed to observe the whole flow characteristics in the compressor. Air and steam were used as working fluids and compared each other to analyze the differences. Although the pressure ratios of fluids showed same tendency, the temperature ratios showed discrepancies each other.