In order to improve the hydraulic efficiency and internal flow pattern of a multi-stage pump under multiple flow conditions, an intelligent optimization design was proposed for its hydraulic components. Sensitivity analysis was used to select the key parameters influencing the hydraulic efficiency of a multi-stage pump. The optimal Latin hypercube sampling and non-dominated sorting genetic algorithm Ⅱ were employed to build a multi-objective optimization system. Moreover, a radial basis function neural network was adopted as the surrogate model of hydraulic efficiency. The research results showed that the impeller outlet width, impeller blade wrap angle, impeller outlet blade angle, and diffuser inlet width were the key factors affecting the hydraulic efficiency. The efficiency of the optimized model increased by 4.35% under the design condition and the matching of the internal flow between the optimized impeller and diffuser was significantly enhanced under the nominal condition. The improved flow pattern could be clearly observed in the flow passage of both the pump impeller and the diffuser. After optimization, the wear performance of the model was also improved compared to the original design. The wear area decreased in size and was distributed more evenly, resulting in a noticeable decrease in the maximum amount of wear.