In　this　paper　we　represent　a　new　numerical　method　for　solving　the　steady　Navier-Stokes　equations　in　three　dimensional　unbounded　domain.　The　method　consists　in　coupling　the　boundary　integral　and　the　finite　element　nonlinear　Galerkin　methods.　An　artificial　smooth　boundary　is　introduced　seperating　an　interior　inhomogeneous　region　from　an　exterior　one.　The　Navier-Stokes　equations　in　the　exterior　region　are　approximated　by　the　Oseen　equations　and　the　approximate　solution　is　represented　by　an　integral　equation　over　the　artificial　boundary.　Moreover,　a　finite　element　nonlinear　Galerkin　method　is　used　to　approximate　the　resulting　variational　problem.　Finally,　the　existence　and　error　estimates　are　derived.