Hydrodynamic performance plays an important role on energy consuming and safety for autonomous underwater vehicles (AUVs). The hydrodynamics of the whole process of AUV free running pushed by a rotating propeller was investigated with physics-based simulations by using multi-block hybrid dynamic grids method, URANS, coupled to 6DOF and UDFs. The AUV had cruised for approximately 14.1 s and 7.105 m from stationary to a constant velocity at 300RPM. The simulation results included an acceleration state and a steady state. In the acceleration state, the thrust decreased quickly and had four periodic cycles in one propeller revolution. The thrust amplitude varied as the velocity increased. The computed velocity history was compared to tests and agreed well. In the steady state, the propulsion factors were compared with that in the literature and agreed well. The flow field variations of pressure and velocity were investigated temporally and spatially for the two states.