Abstract: Harten′s TVD scheme is extented to 2-D general curvilinear coordinates by local rotation matrix translation.A new fully explicit solving method based on Four-Stage Runge-Kutta technique is developed to predict 2-D supersonic and transonic flow field.Comparison between computation and experiment is presented for both supersonic and transonic flow.The numerical results show that this scheme is not only convenient to solve the supersonic flow,but also capable of predicting the transonic flow.