In this paper several planar oblique shock reflection in weakly ionizing,chemically relaxing gas flow have been successfully simulated using a second-order upwind Total Variation Diminishing(TVD) scheme. In present nonequilibrium gas flow calculations the gas-dynamics and species-continuity equations are solved by fully coupling manner,and the fully coupling procedure is described in detail.Numerical solutions are presented with detailed discussion for three examples of oblique shock wave reflection.The numerical results obtained here agree well with the experiments in Refe.[4] by I.I.Glass and calculation results in Refe.[1] H.M.Glaz.