Abstract: A high-efficiency and high-precision CFD method for simulating the unsteady dynamic stall of rotor airfoil has been established based on moving-embedded grid and compressible RANS equations. Firstly, the generation method of viscous and orthogonal body-fitted grid around the rotor airfoil is developed by solving Poisson equations. Meanwhile, aiming at overcoming the shortcoming of spring simulation approach which may result in the distortion of grid, an improved Minimum Distance Method is proposed to generate the embedded grid around airfoil. Secondly, in order to simulate the hysteresis effect of aerodynamic forces caused by the turbulence separation and re-attachment of the flow, a high-precision method on the analysis of unsteady aerodynamic characteristics of rotor airfoil is developed by employing RANS equations and dual-time method. The S-A turbulence model is employed to capture the separation phenomenon of flow around airfoil. Thirdly, according to the conditions of low-speed inflow and high AOAs of the retreating blade, together with the limitation of L-B semi-empirical model on the calculation of unsteady dynamic stall of airfoil, a combination method of Pletcher-Chen preconditioning, FAS multigrid approaches and implicit LU-SGS scheme is established to overcome the problems of convergence difficulty and insufficient precision of compressible equations. The steady, mild and deep dynamic stall cases of NACA0012 and SC1095 rotor airfoils are calculated using this previously mentioned method, the hysteresis effect and the formation, convection, shedding of the vortical disturbance are well captured, the effectiveness of numerical simulation method on dynamic stall is verified. Finally, focus on the deep stall of NACA0012 airfoil, the influence analyses of parameters on the unsteady aerodynamic forces of rotor airfoil are carried out, and the results demonstrate that the exchanges of averaged AOA, amplitude and reduced frequency may cause a variational hysteresis effect and regularly changes of peak value of aerodynamic force.