We　first　analyze　a　stabilized　finite　volume　method　for　the　three-dimensional　stationary　Navier-Stokes　equations.　This　method　is　based　on　local　polynomial　pressure　projection　using　low　order　elements　that　do　not　satisfy　the　inf-sup　condition.　Then　we　derive　a　general　superconvergent　result　for　the　stabilized　finite　volume　approximation　of　the　stationary　Navier-Stokes　equations　by　using　a　L-2-projection.　The　method　is　a　postprocessing　procedure　that　constructs　a　new　approximation　by　using　the　method　of　least　squares.　The　superconvergent　results　have　three　prominent　features.　First,　they　are　established　for　any　quasi-uniform　mesh.　Second,　they　are　derived　on　the　basis　of　the　domain　and　the　solution　for　the　stationary　Navier-Stokes　problem　by　solving　sparse,　symmetric　positive　definite　systems　of　linear　algebraic　equations.　Third,　they　are　obtained　for　the　finite　elements　that　fail　to　satisfy　the　inf-sup　condition　for　incompressible　flow.　Therefore,　this　method　presented　here　is　of　practical　importance　in　scientific　computation.