We　investigate　the　nonlinear　instability　of　a　smooth　steady　density　profile　solution　to　the　three-dimensional　nonhomogeneous　incompressible　Navier-Stokes　equations　in　the　presence　of　a　uniform　gravitational　field,　including　a　Rayleigh-Taylor　steady-state　solution　with　heavier　density　with　increasing　height　(referred　to　the　Rayleigh-Taylor　instability).　We　first　analyze　the　equations　obtained　from　linearization　around　the　steady　density　profile　solution.　Then　we　construct　solutions　to　the　linearized　problem　that　grow　in　time　in　the　Sobolev　space　H　(k)　,　thus　leading　to　a　global　instability　result　for　the　linearized　problem.　With　the　help　of　the　constructed　unstable　solutions　and　an　existence　theorem　of　classical　solutions　to　the　original　nonlinear　equations,　we　can　then　demonstrate　the　instability　of　the　nonlinear　problem　in　some　sense.　Our　analysis　shows　that　the　third　component　of　the　velocity　already　induces　the　instability,　which　is　different　from　the　previous　known　results.