The hydrodynamic performances of a contra-rotating propeller and a contra-rotating rudder propeller are predicted by using the improved delay detached-eddy simulation (IDDES) model and sliding mesh method based on the OpenFOAM software. The thrust coefficients are analyzed by the fast Fourier transform (FFT) method. The numerically calculated thrust coefficients, torque coefficients and propulsion efficiencies of the contra-rotating propeller are compared with the model test results with the errors of 3%, 2% and 5%, respectively, indicating the validity of the numerical method. The numerical results of the contra-rotating rudder propeller show that the pressure drag is the main component of the drag of the pod and strut, and there is a reverse flow at the front of the strut. The strut, therefore, can be optimized from the two aspects. The strut and the pod can also reduce the vibration caused by the bearing force.