The　modified　Maxwell＇s　Steklov　eigenvalue　problem　is　a　new　problem　arising　from　the　study　of　inverse　electromagnetic　scattering　problems.　In　this　paper,　we　investigate　two　finite　element　methods　for　this　problem　and　perform　the　convergence　analysis.　Moreover,　the　monotonic　convergence　of　the　discrete　eigenvalues　computed　by　one　of　the　methods　is　analyzed.