To improve the performance of high specific speed centrifugal pumps and to solve the problem of multi-parameter optimization, an optimal design method based on variable dimensionality reduction and intelligent algorithms was proposed in this paper. The variable dimensionality reduction process was based on the Pearson correlation analysis method, which investigated the influence of eighteen design variables of the impeller on the pump hydraulic performance, and selected eight of them with high influence factors as the final optimization variables. The optimization process was based on the Latin Hypercube Sampling method to generate 160 sets of design samples, and the optimization problem was solved by using artificial neural network and genetic algorithm with maximizing the design working efficiency as the objective. The optimization results are verified by CFD, and the efficiency of the model pump is improved by 3.02% at the design operating point, and the efficient operation zone is broadened; compared with the original impeller, the turbulent kinetic energy distribution in the optimized impeller is improved and the unstable flow structure is reduced.