The upwind scheme exhibits spurious oscillations in resolving the convectively dominated problems. In this paper, a high-resolution scheme for advection equation was developed by using the undetermined coefficient method to reduce the numerical diffusion. The new scheme is applied to a rectangular wave and a Gaussian wave. The results show that the new scheme agrees well with the exact solution for pure convection of a Gauss wave and the rectangular wave. The new scheme has better accuracy than the conventional upwind scheme.