Computational study using the 2-dimensional, compressible, Navier-Stokes equations is performed to predict the discharge coefficient of air flow through a film-cooling hole. In order to investigate the effect of internal/external flows on discharge coefficient, the present computational results which are obtained for three flow cases, only external flow, only internal flow, and no flow, are compared with experimental ones. It is found that the computational results predict the discharge coefficient of the film-cooling hole in a reasonable accuracy and the external crossflow reduces the discharge coefficient, while the internal crossflow increases the discharge coefficient in a range of momentum flux ratio $I_{c-jet}$ > 1 due to the total pressure loss and boundary layer effect.