Firstly, the Fokker?Planck?Kolmogorov equations for nonlinear stochastic dynamic system was studied. Secondly, the third?order TVD Runge?Kutta time difference scheme for differitial equations and the fifth?order WENO scheme for differitial operators were discussed. Moreover, the third?order TVD Runge?Kutta difference scheme was combined with the fifth?order WENO scheme, and the numerical solution for FPK equations using the TVD Runge?Kutta WENO scheme was obtained. Finally, the numerical solution was compared with the analytic solution for FPK equations. The numerical method was shown to give accurate results and overcome the difficulties of other methods, i.e., the probability density function is too small for the peak while too large for the tailed value.