Two-grid　variational　multiscale　(VMS)　algorithms　for　the　incompressible　Navier-Stokes　equations　with　friction　boundary　conditions　are　presented　in　this　article.　First,　one-grid　VMS　algorithm　is　used　to　solve　this　problem　and　some　error　estimates　are　derived.　Then,　two-grid　VMS　algorithms　are　proposed　and　analyzed.　The　algorithms　consist　of　nonlinear　problem　on　coarse　grid　and　linearized　problem　(Stokes　problem　or　Oseen　problem)　on　fine　grid.　Moreover,　the　stability　and　convergence　of　the　present　algorithms　are　established.　Finally,　Numerical　results　are　shown　to　confirm　the　theoretical　analysis.　(C)　2016　Wiley　Periodicals,　Inc.