Research on the wet-steam condensing flow problem is important for improving steam turbine efficiency. This paper derived a total variation diminishing (TVD) discrete method for a two-dimensional curvilinear coordinate system, which discretizes a control equation via a difference scheme that can accurately describe the transonic flow of compressible gas and capture abrupt parameter changes. This method can be applied to improve the shock wave capture accuracy in a cascade passage. A Cascade in White test is chosen as the study object to obtain test data to verify the accuracy of the proposed model. The calculation results indicate that the condensation process has a significant impact on the local flow parameters and that the distribution gradient of the parameters for the liquid phase is relatively large in the condensation position. The degree of subcooling of wet steam is the primary factor that influences the parameter distribution for the liquid phase in the main flow.