This paper presents the design optimization of a centrifugal compressor impeller with a hybrid multi-objective evolutionary algorithm. Reynolds-averaged Navier-Stokes (RANS) equations are solved with the shear stress transport turbulence model as a turbulence closure model. Flow analysis is performed on a hexahedral grid through a finite-volume solver. Two objectives, viz. , the isentropic efficiency and the total pressure ratio (PR), are selected with four design variables that define the impeller hub and shroud contours in meridian terms for optimizing the system. The validation of numerical results was performed through experimental data for the total PR and the isentropic efficiency. Objective-function values are numerically evaluated through the RANS analysis at design points that are selected through the Latin hypercube sampling method. A fast and elitist non-dominated sorting genetic algorithm (NSGA-II) with an epsilon-constraint strategy for local search coupled with a surrogate model is used for multi-objective optimization. The surrogate model, the radial basis neural network, is trained on discrete numerical solutions by the execution of leave-one-out cross-validation for the dataset. The trade-off between the two objectives has been ascertained and discussed in the light of Pareto-optimal solutions. The optimization results show that the isentropic efficiency and the total PR are enhanced at both design and off-design conditions through multi-objective optimization.