In　this　article,　we　consider　a　penalty　finite　element　(FE)　method　for　incompressible　Navier-Stokes　type　variational　inequality　with　nonlinear　damping　term.　First,　we　establish　penalty　variational　formulation　and　prove　the　well-posedness　and　convergence　of　this　problem.　Then　we　show　the　penalty　FE　scheme　and　derive　some　error　estimates.　Finally,　we　give　some　numerical　results　to　verify　the　theoretical　rate　of　convergence.　(c)　2017　Wiley　Periodicals,　Inc.　Numer　Methods　Partial　Differential　Eq　33:　918-940,　2017