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A cratered film-cooling hole was investigated to determine the effect of shape parameters on film-cooling performance, and shape of the hole was optimized to improve film-cooling effectiveness. Numerical analyses were performed using three-dimensional Reynolds-averaged Navier-Stokes (RANS) equations. The numerical results were validated by comparison with experimental data for film-cooling effectiveness for cratered film cooling. The ratio of the major axis length of the crater to the diameter of the hole, the ratio of the minor axis length of the crater to the diameter of the hole, and the ratio of the depth of the crater to the diameter of the hole were chosen as the design variables. From the results of a parametric study, the effects of these three design variables on film-cooling effectiveness were evaluated. The spatially-averaged film-cooling effectiveness was defined as the objective function. The values of the objective function were numerically evaluated through a RANS analysis at the design points determined by Latin hypercube sampling to construct surrogate models, i.e., RSA, RBNN, and Kriging models. Sequential quadratic programming was applied to search for the optimal point from the constructed surrogate models. The result showed that the Kriging model gave best optimization result and the film-cooling effectiveness for a cratered hole was improved by about 20% through the optimization in comparison with the reference geometry.