A　fully　discrete　postprocessing　mixed　finite　element　scheme　is　considered　for　solving　the　time-dependent　Navier-Stokes　equations.　In　the　PP　method,　we　only　consider　a　non-linear　equation　in　the　coarse-level　subspace　and　a　linear　problem　in　the　fine-level　subspace.　The　analysis　shows　that　the　PP　scheme　can　reach　the　same　accuracy　as　the　standard　Galerkin　method　with　a　very　fine　mesh　size　h　by　an　appropriate　choice　of　H.　Numerical　examples　are　provided　that　confirm　both　the　theoretical　analysis　and　the　corresponding　improvement　in　computational　efficiency.