Hydrodynamic analysis and an optimization of a vaned diffuser in a mixed-flow pump are performed in this work. Numerical analysis is carried out by solving three-dimensional Reynolds-averaged Navier-Stokes equations using the shear stress transport turbulence model. A validation of numerical results is conducted by comparison with experimental data for the head, power, and efficiency. An optimization process based on a radial basis neural network model is performed with four design variables that define the straight vane length ratio, the diffusion area ratio, the angle at the diffuser vane tip, and the distance ratio between the impeller blade trailing edge and the diffuser vane leading edge. Efficiency as a hydrodynamic performance parameter is selected as the objective function for optimization. The objective function is numerically assessed at design points selected by Latin hypercube sampling in the design space. The optimization yielded a maximum increase in efficiency of 9.75% at the design flow coefficient compared to a reference design. The performance curve for efficiency was also enhanced in the high flow rate region. Detailed internal flow fields between the reference and optimum designs are analyzed and discussed.