In　this　paper,　we　study　the　convergence　of　time-dependent　Euler-Maxwell　equations　to　incompressible　type　Euler　equations　in　a　torus　via　the　combined　quasi-neutral　and　non-relativistic　limit.　For　well　prepared　initial　data,　the　local　existence　of　smooth　solutions　to　the　limit　equations　is　proved　by　an　iterative　scheme.　Moreover,　the　convergences　of　solutions　of　the　former　to　the　solutions　of　the　latter　are　justified　rigorously　by　an　analysis　of　asymptotic　expansions　and　the　symmetric　hyperbolic　property　of　the　systems.