To quantify the uncertainty of wind turbine airfoil aerodynamic performance under random fluctuation of natural wind, a stochastic numerical analysis model for the aerodynamic characteristics of wind airfoil based on the Transition SST model combining the non-intrusive probabilistic collocation method was established for the S809 airfoil. The determined and uncertain components of aerodynamic characteristics of S809 airfoil under natural wind conditions were obtained. The effects of wind speed and direction uncertainty on the flow field structure, pressure coefficient, friction distribution, and turbulence kinetic energy were quantitated and the uncertainty propagation mechanism was revealed. The results show that the influence of stochastic wind speed and direction on the uncertainty of airfoil lift drag aerodynamic factor is significant. The maximum relative uncertainty of the 3σ confidence interval of lift drag ratio for S809 airfoil within the range of calculated attack angle is ± 35.13%. The uncertainty of lift drag ratio under the coupling effect of stochastic wind speed and direction is 4.76 times and 1.08 times that with single stochastic factor, respectively. The uncertainty sensitive region is observed at the leading edge. Aerodynamic stability optimization design is recommended on the leading edge of the airfoil.