A physics-based simulation for AUV docking with a stationary dock was performed with the multi-block hybrid dynamic grids method (MHDG) and a discretized propeller. URANS equations were coupled to 6DOF equations via UDF to predict the instantaneous velocity and position. The MHDG method uses a multi-block mesh topology, moving mesh, and dynamic-layer method to grid the domain, move the rigid body and its sub domain, and re-mesh the skewed mesh respectively, which can improve computation accuracy and speed. The numerical methods were validated by a comparison with open water curves and the velocity history in AUV free running between simulation and tests. Two docking modes were validated: constant RPM docking and brake docking. In constant RPM docking, the AUV velocity increased gradually, by approximately 11.5% in 6.0 s. The dock had less effect on AUV resistance except that the resistance increased and then declined as the AUV passed through the neck point of the dock. The tip vortex pairs extended and damped downstream of the rotating propeller. In brake docking, the propeller acted as a resistance part and led to a decrement of 46.2% in the velocity in nearly 9 s. The viscous pressure resistance occurred after the braking propeller.