Inthisarticleweconsideratwo-levelfiniteelementGalerkinmethodusingmixedfiniteelementsforthetwo-dimensionalnonstationaryincompressibleNavier-Stokesequations.ThemethodyieldsaH^1-optimalvelocityapproximationandaL^2-optimalpressureapproximation.Thetwo-levelfiniteelementGalerkinmethodinvolvessolvingonesmall,nonlinearNavier-StokesproblemonthecoarsemeshwithmeshsizeH,onelinearStokesproblemonthefinemeshwithmeshsizeh<