We study a three-step two-grid algorithm for solving semiconductor device equations that is discretized by the standard finite element method for the concentration equation and the mixed finite element method for the electric potential equation. The main procedures involve solving the original nonlinear equations on the coarse grid to obtain the initial approximate solution, as well as the linearized equations on the fine grid to obtain a modified solution; furthermore, the calculation on the fine grid is corrected. Error estimation for the method shows that the coarse grid can be much coarser than the fine grid, and the two-grid method still preserves asymptotically optimal approximation. Numerical experiments validate the reliability and effectiveness of the algorithm.