Pump-jet propulsion, a new propulsion technology, is primarily designed for underwater vehicles. Because of its concealment and excellent performance, it has been widely used, but due to its confidentiality and complexity, few studies have been published. To explore the relevant design theory of pump-jet propulsion with the aim of increasing its performance, in this study, we applied the direct and inverse design methods to construct a three-dimensional pump-jet model. The direct design method was carried out by comparing the lifting and lifting-line design methods, followed by further geometric optimization of the better model. In a numerical study using computational fluid dynamics (CFD) simulations, the Reynolds Averaged Naviere-Stokes (RANS) equations with SST k-ω turbulence model were solved in a cylindrical computational domain around the pump-jet propulsion device. A numerical investigation of the E779A propeller was carried out beforehand, using different advance ratios, in order to validate the accuracy of the numerical simulation method. The results show that for the direct method, although the model designed using the lifting-line method produced a greater thrust and the pump-jet designed using the lifting method was more efficient and stable, which is more suitable for small and medium underwater vehicles. When considering the inverse design method, the pump-jet propeller obviously accelerated the fluid, and the speed was obviously greater than that designed using the direct design method, while the turbulent kinetic energy in the flow field was higher, as well as the energy loss. Therefore, for small- and medium-sized underwater vehicles, if the priorities are high thrust and high efficiency, the inverse design method is the best option, whereas if stability and lower energy loss are preferred, the direct design method should be adopted.