Two-dimensional transonic cascade flows of gas-liquid droplet mixture are calculated using the solution-adaptive unstructured grid for the steady gas-only phase and the iterative particle-source-in-cell method for the gas-particle coupling. Roe's flux difference splitting method is used to solve the Euler equations, whereas the liquid droplets are traced by the Lagrangian method using the rebound/breakup impact model. To verify accuracy of the computer code, the Jet Propulsion Laboratory nozzle is first calculated for the gas-solid particle mixture. The transonic flow in the NACA 65410 cascade passage is then solved to estimate the effect of liquid droplets on the aerodynamic performance.