Numerical study is reported of a turbulent flow and a convective heat transfer rate around a gas turbine blade. In the computation of turbulent flow, a hybrid method of the central and the upwind finite differencing is used with the standard k-e turbulence model. The quasi-linear transformed coordinate is adopted for a grid system. For the computation of wall boundaries, the wall function is based on the idea that, beyond the viscous sublayer, the turbulent length scale is universal, increasing linearly with distance from the wall. The computed results display more effects of free stream turbulence level on the suction side where a strong favorable pressure gradient takes place than on the pressure side. The model illustrated here shows results superior to the analytic solution as a whole.