Spectral　Galerkin　approximation　problem　of　bifurcation　point　of　the　Navier-Stokes　equations　is　studied.　By　analyzing　property　of　simple　bifurcation　point,　the　extended　system　and　its　spectral　Galerkin　approximation　extended　system　of　nondegenerate　simple　bifurcation　point　of　the　Navier-Stokes　equations　are　constructed.　The　existence　and　convergence　of　solutions　of　the　approximation　extended　system　are　proved,　moreover,　the　error　estimations　of　spectral　approximation　are　given　by　using　eigenvalue　of　Stokes　operator.　Because　the　derivation　of　the　extended　system　has　a　block　lower　triangular　form,　the　method　of　splitting　iteration　is　applied　to　compute　simple　bifurcation　point,　not　only　computational　work　is　reduced,　but　also　local　quadratic　convergence　is　achieved.　Accordingly,　the　valid　algorithm　for　nondegenerate　simple　bifurcation　point　of　the　Navier-Stokes　equations　is　given.