A low order characteristic‐nonconforming finite element method is proposed for solving a two‐dimensional convection‐dominated transport problem. On the basis of the distinguish property of element, that is, the consistency error can be estimated as order O(h2), one order higher than that of its interpolation error, the superclose result in broken energy norm is derived for the fully discrete scheme. In the process, we use the interpolation operator instead of the so‐called elliptic projection, which is an indispensable tool in the traditional finite element analysis. Furthermore, the global superconvergence is obtained by using the interpolated postprocessing technique. Lastly, some numerical experiments are provided to verify our theoretical analysis. Copyright © 2013 John Wiley & Sons, Ltd.