We　study　the　stability　of　smooth　solutions　near　non-constant　equilibrium　states　for　a　bipolar　full　compressible　Navier-Stokes-Maxwell　system　in　a　threedimensional　torus　T　=　(R/Z)(3).　This　system　is　quasilinear　hyperbolic-parabolic.　In　the　first　part,　by　using　the　maximum　principle,　we　find　a　non-constant　steady　state　solution　with　small　amplitude　for　this　system.　In　the　second　part,　with　the　help　of　suitable　choices　of　symmetrizers　and　classic　energy　estimates,　we　prove　that　global　smooth　solutions　exist　and　converge　to　the　non-constant　steady　states　as　the　time　goes　to　infinity.　As　a　byproduct,　we　obtain　the　global　stability　for　the　bipolar　full　compressible　Navier-Stokes-Poisson　system.