This article focuses on the propulsion characteristics of the pump-jet propulsor (PJP) behind the hull and the influence of the main dimensions of the duct. The flow fields of the PJP behind the hull under different ship speeds, rotational velocities and main dimensions of the duct are solved by the Improved Delayed Detached Eddy Simulation (IDDES) method to provide the selection ranges of the main dimensions of the duct based on the propulsion efficiency and the propulsor power. It investigates the propulsion performance of the PJP and the self-propulsion factors under different ship speeds and main dimensions of the duct including the inclination angle, axial length, maximum thickness, inlet diameter, and outlet diameter. The results show that except for the duct maximum thickness, the inclination angle, axial length, inlet diameter, and outlet diameter of the duct have significant impacts on the self-propulsion factors and the power. The variation of the inclination angle and the outlet diameter significantly change the flow rate of the propulsor, thereby affecting the propulsion efficiency and the power. It indicates that when determining the main parameters of the duct of the PJP for a submarine, except for proper selection of the values within reasonable ranges, the inclination angle and outlet diameter should also be optimized based on the shape and angle of the hull stern.