In this paper, shape optimization based on three-dimensional flow analysis has been performed for impeller design of centrifugal compressor. To evaluate the objective function of an isentropic efficiency, Reynolds-averaged Navier-Stokes equations are solved with SST (Shear Stress Transport) turbulence model. The governing equations are discretized by finite volume approximations. The optimization techniques based on the radial basis neural network method are used for the optimization. Latin hypercube sampling as design of experiments is used to generate thirty design points within design space. Sequential quadratic programming is used to search the optimal point based on the radial basis neural network model. Four geometrical variables concerning impeller shape are selected as design variables. The results show that the isentropic efficiency is enhanced effectively from the shape optimization by the radial basis neural network method.