In　this　paper,　we　consider　the　pressure　projection　stabilized　finite　element　method　for　the　Navier-Stokes　equation　with　nonlinear　slip　boundary　conditions　whose　variational　formulation　is　the　variational　inequality　problem　of　the　second　kind　with　Navier-Stokes　operator.　The　H　(1)　and　L　(2)　error　estimates　for　the　velocity　and　the　L　(2)　error　estimate　for　the　pressure　are　obtained.　Finally,　the　numerical　results　are　displayed　to　verify　the　theoretical　analysis.