Unsteady transonic flows with condensation through steam turbine stator-rotor channels are numerically predicted by using the numerical method developed by our group. Fundamental equations solved here consist of conservation laws of mixed gas, water vapor, water liquid, and the number density of water droplets, coupled with the momentum equations and the energy equation. Also the shear-stress transport (SST) turbulence model is employed to predict the turbulent quantities. The numerical method is based on the high-order high-resolution finite-difference method. The fourth-order monotone upstream-centered schemes for conservation laws (MUSCL) with the total variation diminishing (TVD) scheme, Roe's approximate Riemann solver, and the lower-upper symmetric Gauss-Seidel (LU-SGS) scheme are employed in the numerical method. As numerical examples, transonic condensate flows of moist air through a turbine and a compressor cascade channel are first calculated. Also wet-steam turbine stator-rotor cascade channels are calculated assuming homogeneous and heterogeneous condensations.