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To improve the efficiency of residual heat removal pump, 35 impellers, whose design variables are the radius of shroud arc, radius of hub arc, angle of shroud and angle of hub, were designed by Latin hypercube sampling method. 3D steady simulation was conducted to get the efficiency under designed flow rate by ANSYS CFX 14.5 software. A radial basis neural network was used to build the approximation model between efficiency and design variables. Finally, the best combination of the design variables was obtained by solving the approximation model with genetic algorithm. The results showed that performance curve simulated by CFD had a good agreement with that of experiment. The deviations of efficiency and head between numerical result and experimental result were -2.1% and -3.7%, respectively. Compared the efficiency predicted by CFD with that predicted by radial basis neural network, the deviation was only 0.02%, thus the radial basis neural network can predict the efficiency under design condition accurately. The efficiency of the optimal pump was 76.75% and the optimization made an increase in efficiency by a percentage of 6.18. The optimization improved the velocity and turbulence kinetic energy distributions in the impeller. The vortexes disappeared and the velocity became uniform at the shroud. Thus, the optimization process for the impeller meridional shape was practical.