Hovering is one of important statuses to evaluate the aerodynamic performance of a rotor. With the development of the computer technology and CFD technique, the numerical methods based on the first principle are usually employed to evaluate the hovering performance of the rotor. The transition process will evidently affect the results from the RANS-based numerical simulations in some steady cases for the fixed wing aircrafts, which should be taken into consideration in the design process. But it's not clear whether the transition process would affect the numerical results for the rotor simulation. To provide the reference in designing and evaluating the rotorcraft, the effect of the transition process in the rotor simulation needs to be discussed further. The PSP rotor proposed by NASA is calculated using the in-house solver based on the overset grid in this paper. Simulations are performed with fully turbulent model as well as the transitional model and the results are compared to the experimental data. The results prove the superior ability to simulate the flow around a hovering rotor of the in-house solver. The relative errors of the numerical results are under 5%. The range of the laminar flow on the blade is proportional to the rotor thrust, which causes a higher Figure of Merit in transition simulation than the fully turbulent simulation. The sectional pressure distribution and torque distribution along the blade apparently suffer from the transition process, which doesn't affect the thrust distribution along the blade and the blade vortex wake flow under the rotor disk. An obvious flow separation on the surface of the blade can be observed in the transition simulation compared to the fully turbulent simulation.