We　investigate　the　nonlinear　instability　of　a　smooth　Rayleigh-Taylor　steady-state　solution　(including　the　case　of　heavier　density　with　increasing　height)　to　the　three-dimensional　incompressible　nonhomogeneous　magneto-hydrodynamic　(MHD)　equations　of　zero　resistivity　in　the　presence　of　a　uniform　gravitational　field.　We　first　analyze　the　linearized　equations　around　the　steady-state　solution.　Then　we　construct　solutions　of　the　linearized　problem　that　grow　in　time　in　the　Sobolev　space　H　k　,　thus　leading　to　the　linear　instability.　With　the　help　of　the　constructed　unstable　solutions　of　the　linearized　problem　and　a　local　well-posedness　result　of　smooth　solutions　to　the　original　nonlinear　problem,　we　establish　the　instability　of　the　density,　the　horizontal　and　vertical　velocities　in　the　nonlinear　problem.　Moreover,　when　the　steady　magnetic　field　is　vertical　and　small,　we　prove　the　instability　of　the　magnetic　field.　This　verifies　the　physical　phenomenon:　instability　of　the　velocity　leads　to　the　instability　of　the　magnetic　field　through　the　induction　equation.