The performance of a louver cooling scheme on a transonic airfoil has been studied numerically in this paper. Film cooling holes are located near the passage throat. The Mach number at the location of the jet exit is close to unity. A comparison of film cooling effectiveness between numerical prediction and experimental data for a circular hole shows that the numerical procedures are adequate. In addition to the shock wave effects and compressibility, curvature effect was also studied by comparing cooling effectiveness on the airfoil surface with that on a flat plate. Substantially higher cooling effectiveness for the louver cooling scheme on the airfoil was predicted at blowing ratios below 1 in comparison to other cooling configurations. At higher blowing ratios than 2 the advantages of the louver cooling scheme becomes less obvious. It was also found that for the same cooling configuration the cooling effectiveness on the transonic airfoil is slightly higher than that on a flat plate at moderately low blowing ratios below 1. At high blowing ratios above 2 when the oblique shock becomes detached from the leading edge of the hole exits, dramatic reduction in cooling effectiveness occurs as a result of boundary layer separation due to the strong shock waves. A coolant-blockage and shaped-wedge analogy was proposed and found to be able to qualitatively explain this phenomenon satisfactorily.