This paper presents a procedure for the design optimization of a centrifugal compressor. The centrifugal compressor consists of a centrifugal impeller, vaneless diffuser and volute. And, optimization techniques based on the radial basis neural network method are used to optimize the impeller of a centrifugal compressor. The Latin-hypercube sampling of design-of-experiments is used to generate the thirty design points within design spaces. Three-dimensional Reynolds-averaged Navier-Stokes equations with the shear stress transport turbulence model are discretized by using finite volume approximations and solved on hexahedral grids to evaluate the objective function of the total-to-total pressure ratio. Four variables defining the impeller hub and shroud contours are selected as design variables in this optimization. The results of optimization show that the total-to-total pressure ratio of the optimized shape at the design flow coefficient is enhanced by 2.46% and the total-to-total pressure ratios at the off-design points are also improved significantly by the design optimization.