In the present study, numerical simulations of the PSP rotor in hover are conducted by using a Reynolds-averaged Navier-Stokes CFD flow solver based on unstructured meshes. The calculations are made of a collective pitch angle from 4 to 12 degrees with an interval of 2 degrees at two blade tip Mach numbers of 0.585 and 0.65. The improved γ-Reθt-CF+ model is adopted for predicting laminar-turbulent onset phenomena involving crossflow induced transition. To further investigate the effects of the γ-Reθt-CF+ transition model, flow simulations are also carried out using the baseline γ-Reθt model and the kω-SST fully turbulent model. The predicted results such as transition onset locations and rotor aerodynamic performances in terms of thrust coefficient, torque coefficient and figure of merit are compared with experimental data. The change of transition onset position depending on the blade tip Mach number of 0.585 and 0.65 is also investigated.