In this paper, the hydrodynamic characteristics of a rim-driven thruster (RDT) behind the hull of an underwater vehicle are investigated. The studied underwater vehicle is the benchmark DARPA (Defense Advanced Research Projects Agency) suboff model, with and without full appendages. In order to verify and validate the numerical model, a grid sensitivity analysis is made for the AFF-1, AFF-8 and the ducted propeller cases, respectively. Then, the resistance and pressure distribution over the surface of the suboff with and without appendages are compared with available experimental measurements and good correlations were observed. As for the propeller, a well-studied ducted propeller, the 19A duct in combination with Ka-47 blades, is employed, and the numerical results exhibit a close relationship with the available experimental data under a wide range of advance coefficients. Afterwards, the self-propulsion characteristics of the suboff models propelled by RDTs using different duct configurations are studied, more specifically, the unsteady effects of the flow field induced by the interactions between propeller and hull under various working conditions. The results indicate that due to the influence of the hull, the RDTs operate in different working conditions compared to open water and exhibit distinct hydrodynamic characteristics. Moreover, the duct profile can have a significant effect on the unsteady pressure fluctuations in the flow field, especially in the vicinity of the propeller.