In　this　article　we　consider　a　spectral　Galerkin　method　with　a　semi-implicit　Euler　scheme　for　the　two-dimensional　Navier-Stokes　equations　with　H-2　or　H-1　initial　data.　The　H-2-stability　analysis　of　this　spectral　Galerkin　method　shows　that　for　the　smooth　initial　data　the　semi-implicit　Euler　scheme　admits　a　large　time　step.　The　L-2-error　analysis　of　the　spectral　Galerkin　method　shows　that　for　the　smoother　initial　data　the　numerical　solution　u(m)(n)　exhibits　faster　convergence　on　the　time　interval　[0,　1]　and　retains　the　same　convergence　rate　on　the　time　interval　[1,　infinity).　(c)　2005　Wiley　Periodicals,　Inc.