A　fully　discrete　two-level　finite　element　method　(the　two-level　method)　is　presented　for　solving　the　two-dimensional　time-dependent　Navier-Stokes　problem.　The　method　requires　a　Crank-Nicolson　extrapolation　solution　(u(H,tau0),　p(H,tau0))　on　a　spatial-time　coarse　grid　J(H,tau0)　and　a　backward　Euler　solution　(u(h,tau),　p(h,tau))　on　a　space-time　fine　grid　J(h,tau).　The　error　estimates　of　optimal　order　of　the　discrete　solution　for　the　two-level　method　are　derived.　Compared　with　the　standard　Crank-Nicolson　extrapolation　method　(the　one-level　method)　based　on　a　space-time　fine　grid　J(h,tau),　the　two-level　method　is　of　the　error　estimates　of　the　same　order　as　the　one-level　method　in　the　H-1-norm　for　velocity　and　the　L-2-norm　for　pressure.　However,　the　two-level　method　involves　much　less　work　than　the　one-level　method.