To investigate the impact of different computational strategies on the self-propulsion hydrodynamic performance of a submarine model, a study was conducted using the RANS method, employing both the steady-state Moving Reference Frame (MRF) method and the unsteady Rigid Body Motion (RBM) method. Numerical simulations of the self-propulsion hydrodynamic performance of the submarine model were performed under different computational strategies, including submarine with propeller, submarine first and propeller second, and propeller rotational speed iteration. The differences between these strategies were analyzed from various perspectives, such as submarine resistance, propeller hydrodynamic performance, total solver actual runtime, propeller unsteady bearing forces, and induced fluctuating pressure. The results indicated that when conducting numerical simulations of the self-propulsion hydrodynamic performance of the submarine with a propeller, the fluctuation ranges of the submarine resistance, propeller thrust, and torque obtained by the steady MRF method were within 0.1% to 0.8%, compared with the three strategies in the unsteady state. In terms of computational efficiency, strategy 3 (RBM—submarine with a propeller) had the lowest computational efficiency, and the time to obtain a self-propulsion curve was 11.9 times, 4.4 times, and 3.1 times that of strategy 1 (MRF + RBM—submarine with a propeller), strategy 2 (RBM—submarine first, then propeller), and strategy 4 (RBM—propeller rotational speed iteration). When analyzing the propeller excitation forces under the submarine’s self-propulsion state using the steady-state MRF method combined with the unsteady RBM method, the frequency domain peak fluctuations were within 5% compared with the three strategies in the unsteady state, making this method suitable for numerical simulations of propeller excitation forces. These findings provide methodological support for evaluating the performance of the submarine’s hydrodynamic propulsion system.