The propulsion and vortical flow of a preswirl pump-jet propulsor (PJP) under effective wake conditions are numerically investigated by improved delayed detached eddy simulation. The numerical results agree well with the experiments. The effects of the interaction between the hull and PJP on the propulsion performance and flow characteristics are discussed in detail, particularly the effects on the flows around the duct and the stator. Results show that the PJP performance changes noticeably owing to the hull-retarded flow. The rotor forces are mainly changed due to the effective velocity magnitude of the PJP oncoming flow, while the flow direction does not show notable effects as the duct and stator notably improve the rotor oncoming flow. The appendage wake notably increases the thrust fluctuation of the rotor, causing dominant fluctuation components at low frequencies. The thrusts on the duct and stator are sensitive to the direction of the PJP oncoming flow, as the flows around them change considerably when the flow direction changes. The flow direction affects the velocity and pressure distribution of the duct and the generation and evolution of vortices in the stator region. The forward stagnation point on the duct plays a crucial role in duct thrust, around flow, and in the flow into the duct. The stator improves the uniformity of the rotor inflow during preswirling of the flow under effective wake conditions, which is very important for a submarine-applied PJP. The interaction between the hull and PJP is very complex.