In　this　paper,　we　use　divergence-free　wavelets　to　give　an　adaptive　solution　to　the　velocity　field　of　the　Stokes　problem.　We　first　use　divergence-free　wavelets　to　discretize　the　divergence-free　weak　formulation　of　the　Stokes　problem　and　obtain　a　discrete　positive　definite　linear　system　of　equations　whose　coefficient　matrix　is　quasi-sparse;　Secondly,　an　adaptive　scheme　is　used　to　solve　the　discrete　linear　system　of　equations　and　the　error　estimation　and　complexity　analysis　are　given.　©　2007　Editorial　Board　of　Analysis　in　Theory　and　Applications.