A two‐grid method is presented and discussed for a finite element approximation to a nonlinear parabolic equation in two space dimensions. Piecewise linear trial functions are used. In this two‐grid scheme, the full nonlinear problem is solved only on a coarse grid with grid size H. The nonlinearities are expanded about the coarse grid solution on a fine gird of size h, and the resulting linear system is solved on the fine grid. A priori error estimates are derived with the H1‐norm O(h + H2) which shows that the two‐grid method achieves asymptotically optimal approximation as long as the mesh sizes satisfy h = O(H2). An example is also given to illustrate the theoretical results.