An highly efficient and fast numerical solution, i.e. two-grid finite volume element method, has been constructed for the solution of the steady linear Schr dinger equation. With the solution domain divided into coarse and fine grids, an initial acquisition of the finite volume element solution of the original problem can be achieved on the coarse grid, followed by the solution of a decoupling problem on the fine grid. The numerical example verifies the improved solving efficiency in the proposed scheme. It has also been theoretically proven that the solution is characterzied with the same convergence order as the finite volume element solution of the original problem.