In view of a solution of the two-dimensional linear Schr?dinger equation, a new semi-discrete finite element two-grid algorithm has thus been constructed. The finite element solution of the Schr?dinger equation originally solved on a fine grid is simplified to first solve the finite element solution of the original equation on a coarse grid, followed by the adoption of the numerical solution obtained on the coarse grid to decouple the real and imaginary parts of the equation on the fine grid, thus solving the finite element solutions of two elliptical equations. An analysis has been made of the error between the finite element solution of two grids and the exact solution under the H1 norm, with numerical experiments conducted. The numerical results show that the error order remains the same as that in reference [10], with the error smaller at different times.