In this presentation, I will talk about the convergence for the inverse problem of the 2-D semi-discrete Schrödinger equation with one observation on the partial boundary. First, an energy estimate for the semi-discrete Schrödinger equation is given. Then the uniform Lipschitz stability for the inverse coefficient problem of the semi-discrete Schrödinger equation is proved. Finally, with the Lax equivalence theorem for the applied second-order finite difference scheme, we conclude the convergence of the semi-discrete inverse problem.