In　this　paper,　we　consider　the　flow　between　two　concentric　rotating　spheres,　and　use　Legendre　and　adjoint　Legendre　functions　to　approximate　r　and　θ　directions,　respectively,　thus　construct　the　full　discrete　Legendre-Galerkin　spectral　scheme,　and　derive　the　stability　conditions　and　its　error　estimate.