©　2018　Springer　Science+Business　Media,　LLC,　part　of　Springer　Nature　In　this　paper　a　unified　nonconforming　virtual　element　scheme　for　the　Navier-Stokes　equations　with　different　dimensions　and　different　polynomial　degrees　is　described.　Its　key　feature　is　the　treatment　of　general　elements　including　non-convex　and　degenerate　elements.　According　to　the　properties　of　an　enhanced　nonconforming　virtual　element　space,　the　stability　of　this　scheme　is　proved　based　on　the　choice　of　a　proper　velocity　and　pressure　pair.　Furthermore,　we　establish　optimal　error　estimates　in　the　discrete　energy　norm　for　velocity　and　the　L2　norm　for　both　velocity　and　pressure.　Finally,　we　test　some　numerical　examples　to　validate　the　theoretical　results.