The finite element formulation of the Maxwell equation is derived by using the edge finite element method and is used to simulate the 3-D electromagnetic responses to the subspace medium.Through the definition of the electric field in the edge of each cell,the problem of the discontinuity of the tangential components of the electric field between different cells in node finite element method is solved and this method also keeps the property of the non-divergence and finite rotation.The separation of the total electric field into the background and the secondary fields makes it possible that the technique proposed in the paper is suitable for the magnetic dipole in any direction.The properties of the convergence of seven Krylov subspace iterative solvers and the effectiveness of the incomplete Cholesky decomposition pre-conditioner are analyzed through two simulation examples.Comparisons of different solvers show that the generalized productive bi-conjugate gradient iterative solver processed with pre-conditioner has the best convergence and it is the best selection in 3-D electromagnetic modeling.