©　2005,　Springer　Verlag.　All　rights　reserved.Two-level　finite　element　approximation　to　stream　function　form　of　unsteady　Navier-Stokes　equations　is　studied.　This　algorithm　involves　solving　one　nonlinear　system　on　a　coarse　grid　and　one　linear　problem　on　a　fine　grid.　Moreover,the　scaling　between　these　two　grid　sizes　is　super-linear.　Approximation,　stability　and　convergence　aspects　of　a　fully　discrete　scheme　are　analyzed.　At　last　a　numrical　example　is　given　whose　results　show　that　the　algorithm　proposed　in　this　paper　is　effcient.