We recently proposed a numerical method for simulating flows of supercritical CO2 based on a preconditioning method and the thermophysical models programed in a program package for thermophysical properties of fluids (PROPATH). In this study, this method is applied to the investigation of cascade channel. Numerical results obtained by assuming supercritical pressure conditions indicate that the normal shock generated in the cascade channel deeply depends on the pressure condition. In particular, the speed of sound varying with the pressure variation at the supercritical state is a key thermophysical property which changes the flow field in the cascade channel. In addition, we also simulate those flows with nonequilibrium condensation in which the inlet pressure and temperature approaching to those of the critical point are specified. Then a nonequilibrium condensation model developed by our group is further applied to the numerical method. CO2 condensation observed in a case indicates that condensation occurs at a local region near the leading edge due to the flow expansion; the droplets soon grow at the local region and streams downward with keeping almost the same mass fraction.