We present a scheme for solving two-dimensional semilinear reaction-diffusion equations using a expanded mixed finite element method. To linearize the mixed-method equations, we use a two grid algorithms based on the Newton iteration method. The solution of nonlinear system on the fine space is reduced to the solution of two small (one linear and one nonlinear) systems on the coarse space and a linear system on the fine space. It is shown that the coarse grid can be much coarser than the fine grid and achieve asymptotically optimal approximation as long as the mesh sizes satisfy H=O (h13). As a result, solving such a large class of nonlinear equation will not be much more difficult than solving one single linearized equation.