Abstract: A time-split explicit TVD MacCormack algorithm is used to solve the two-dimensional N-S equations coupled with species diffusion equations.Both molecular and turbulent properties of viscosity,thermal conductivity and mass conductivity are calculated.In order to deal with the near wall separation of boundary layer,the low Reynolds number ｋ-ε turbulence model of Lam and Bremhorst is used in this procedure.A sample of plane cross-flow is used to test the reliability and accuracy of this method and the results show that this scheme can be applied to solve the problem of supersonic flow fields with gas mixing,the solutions are satisfactory.