The　bipolar　compressible　Euler-Maxwell　equations　as　a　hydrodynamic　model　arising　from　plasma　physics　to　describe　the　dynamics　of　the　compressible　electrons　and　ions　was　investigated.　This　work　was　concerned　with　three-dimensional　Euler-Maxwell　equations　with　smooth　periodic　solutions.　With　the　help　of　energy　method　and　the　energy　functional　convex　method,　the　global　smooth　solution　with　small　amplitude　was　established　near　a　constant　equilibrium　solution　with　asymptotic　stability　property.