The aerodynamic performance of the floating offshore wind turbine has an extra level of complexity than that of bottom-fixed wind turbines because of the motions of the supporting platform. In this paper, the unsteady aerodynamic performance of the NREL-5MW Baseline wind turbine with periodical surge and pitch motions of its supporting platform are investigated. The three-dimensional Reynolds Averaged Navier-Stokes equations are solved for the aerodynamic numerical simulation. The naoe-FOAM-os-SJTU solver, which is based on OpenFOAM and overset grid technology and developed for ship and ocean engineering problems, is employed. From the simulation, the time series of the unsteady torque and thrust are obtained, together with the detailed information of the wake flow field, and the pressure coefficient distribution in different cross-section are also available to clarity the detailed flow filed information. The simulation results are compared both with those obtained from aerodynamic simulation of wind turbine without effects of platform motions, and with other approaches in previous studies. The simulation results show that the pitch motion has more significant effects on the aerodynamic forces and moments of the rotor than the surge motion does. And the motion of the platform especially the pitch motion may bring very bad influence on the turbine forces and wake flow, even on the power generation in case of very severe pitch motion.