Abstract: As a finite element scheme to solve convection-diffusion equations, the upwind factor method is presented, which introduces an optimum upwind factor to ensure the stability at any Peclet number. It neither changes the location of Gauss points along the stream line, nor adopts unsymmetri-cal shape function to discretize the convection term. It features simplicity in concept, efficiency in convergence, rather high accuracy and stability since it introduces the artificial diffusion necessary not only for the stability but also for the accuracy of computation.Numerical experiments demonstrate that the scheme is very robust at any Peclet number, it converges very fast with relaxation factor up to 1. 0, and the scheme introduces less false diffusion than Spalding's, so its results approximate to the analytical ones.