An unsteady aerodynamics model based on the Beddoes-Leishman type dynamic stall model in a state-space formulation was presented to predict the unsteady aerodynamic forces on an airfoil undergoing arbitrary motion. According to the operating condition of wind turbine airfoils, the compressibility effects and flow separation initiated from the leading edge were neglected. The model includes the effects of near wake and the effects of trailing edge separation. Four aerodynamic states were adopted to describe the dynamics of the unsteady aerodynamic force coefficients: two states were applied to model the time-lag of the near wake effect, and the other two states were used to model the time-lag effect of trailing edge separation. Applying the proposed model, unsteady aerodynamic forces of a FFA-W3-241 wind turbine airfoil during harmonic pitching motion were calculated. The calculation results showed a good agreement with the experimental data, which indicated that the proposed model ould preferably model the unsteady aerodynamic characteristics of wind turbine airfoils. The numerical dynamic stall module was integrated into a wind turbine aerodynamics and structural dynamics analysis software. Applying the software, a simulation of power production load case of a 1.5 MW variable-speed pitch-regulated wind turbine was carried out. The simulation results indicate that unsteady aerodynamic characteristics of airfoils shall be taken into account during wind turbine design process because they significantly affect the transient aerodynamic loads of the rotor.