The non-uniform inflow caused by the elbow inlet is one of the main reasons for the low actual operation performance of a centrifugal pump. Orthogonal experiment and GA_PSO algorithm are used to improve the head and efficiency of a centrifugal pump with an elbow inlet based on the method combining numerical simulation and prototype experiment in this paper. The effects of the design parameters, including elbow inlet radius ratio, blade inlet angle, blade number, blade wrap angle, blade outlet angle, impeller outlet diameter, blade outlet width and flow area ratio, on the pump head and efficiency are studied in the orthogonal experiment. The blade inlet angle is the major factor to match the non-uniform inflow and reduce the flow loss in the impeller inlet to contribute to enhancing the pump performance and cavitation characteristics. The particle swarm optimization (PSO) algorithm is optimized by integrating the genetic algorithm (GA), which ensures that the PSO-calculation result avoids falling into the local optimization and the global optimal solution is obtained as quickly as possible. The centrifugal pump with an elbow inlet is optimally designed by the GA_PSO algorithm. According to the performance test results, the efficiency of the optimized pump is 4.7% higher than that of the original pump.