In　this　paper,　we　introduce　a　finite　volume　element　method　for　the　Navier-Stokes　problem.　This　method　is　based　on　the　multiscale　enrichment　and　uses　the　lowest　finite　element　pair　P-1/P-0.　The　stability　and　convergence　of　the　optimal　order　in　H-1-norm　for　velocity　and　L-2-norm　for　pressure　are　obtained.　Using　a　dual　problem　for　the　Navier-Stokes　problem,　we　establish　the　convergence　of　the　optimal　order　in　L-2-norm　for　the　velocity.