This study presents a numerical procedure to optimize the shape of cylindrical cooling hole to enhance film-cooling effectiveness. The RBNN method is used as an optimization technique with Reynolds-averaged Navier-Stokes analysis of fluid flow and heat transfer with shear stress transport turbulent model. The hole length-to-diameter ratio and injection angle are chosen as design variables and film-cooling effectiveness is considered as objective function which is to be maximized. Twelve training points are obtained by Latin Hypercube Sampling for two design variables. In the sensitivity analysis, it is found that the objective function is more sensitive to the injection angle of hole than the hole length-to diameter ratio. Optimum shape gives considerable increase in film-cooling effectiveness.