The　nonlinear　Galerkin　methods　are　numerical　schemes　for　evolutionary　partial　differential　equations　based　on　the　theory　of　inertial　manifolds　and　approximate　inertial　manifolds.　In　this　paper,　we　consider　the　flow　between　two　concentric　rotating　spheres,　and　combine　the　Legendre-Galerkin　spectral　methods　in　Part　I　together　with　the　nonlinear　Galerkin　method,　then　construct　the　full　discrete　nonlinear　Legendre-Galerkin　spectral　scheme,　and　derive　the　stability　conditions　and　its　error　estimate.