Submersible pumps are now in high demand due to the sporadic occurrence of recent torrential rains. The current study was carried out to investigate the hydraulic characteristics of a submersible axial-flow pump with a swept impeller and to optimize the impeller and diffuser shapes of the pump to enhance the hydraulic performance. Three-dimensional Reynolds-averaged Navier–Stokes equations were solved with the shear stress transport turbulence model. The governing equations were discretized using the finite volume method, and unstructured tetrahedral and hexahedral meshes were used in the grid system. The optimal grid system was selected through a grid dependency test. A performance test for the submersible axial-flow pump was carried out experimentally, and the results of the numerical analysis were validated against the experimental results. The hydraulic efficiency and the total head were used as objective functions. For the first optimization, a multi-objective optimization was carried out to simultaneously improve the objective functions through a hybrid multi-objective evolutionary algorithm coupled with a response surface approximation by varying the swept angle and pitch angle of the blades of the rotating impeller. The second multi-objective optimization was performed using two design variables, i.e., the inlet angle and the length of the diffuser vanes, to simultaneously increase the objective functions. Clustered optimum designs in the Pareto optimal solutions yielded significant increases in the objective function values as compared with the reference design.