In the present study, numerical simulations of the PSP rotor in hover were carried out by using a Reynolds-averaged Navier-Stokes CFD flow solver based on unstructured mixed + meshes. The improved γ-Reθ t-CF model was adopted for the prediction of laminar-turbulent onset phenomena involving crossflow induced transition and flow separation. In order to capture vortex with high resolution, an improved scheme ESWENO-P was used for computing the inviscid fluxes on Cartesian meshes. The predicted results such as transition onset locations and rotor aerodynamic performances in terms of thrust coefficient, torque coefficient and figure of merit were compared with experimental data. The effects of the fuselage and facility walls on PSP rotor performance in hover were also investigated.