In　this　paper　we　study　a　new　local　stabilized　nonconforming　finite　element　method　based　on　two　local　Gauss　integrals　for　solving　the　stationary　Navier-Stokes　equations.　This　nonconforming　method　utilizes　the　lowest　equal-order　pair　of　mixed　finite　elements　(i.e.,　NCP1-P-1).　Error　estimates　of　optimal　order　are　obtained,　and　numerical　results　agreeing　with　these　estimates　are　demonstrated.　Numerical　comparisons　with　other　mixed　finite　element　methods　for　solving　the　Navier-Stokes　equations　are　also　presented　to　show　the　better　performance　of　the　present　method.　(C)　2010　Elsevier　B.V.　All　rights　reserved.