A fan-shaped hole for film cooling has been studied to find the effect of geometric variations on the cooling performance and optimized to enhance film-cooling effectiveness using three-dimensional Reynolds-averaged Navier-Stokes analysis and surrogate approximation methods. The computational results for film-cooling effectiveness using SST turbulence model have been validated in comparison with the experimental data. The injection angle, lateral expansion angle, and ratio of length-to-diameter of the hole are chosen as the design variables, and the effects of these variables on the cooling performance are evaluated. To optimize a fan-shaped hole, the spatially-averaged film-cooling effectiveness is considered as the objective function, which is to be maximized. Latin hypercube sampling is used to determine the training points as a means of the design of experiment. A weighted-average surrogate model is used to approximate the data generated by numerical analysis at the design points. And, sequential quadratic programming is used to search for the optimal point from the constructed surrogate. The results of the optimization show that the film-cooling effectiveness has been successfully improved through optimization, when compared with the reference geometry. (C) 2010 Elsevier Ltd. All rights reserved.