The　concept　of　g-frame　and　g-Riesz　basis　in　a　complex　Hilbert　space　was　introduced　by　Sun.18　In　this　paper,　we　generalize　the　g-frame　and　g-Riesz　basis　in　a　complex　Hilbert　space　to　a　complex　Banach　space.　Using　operators　theory　and　methods　of　functional　analysis,　we　give　some　characterizations　of　a　g-frame　or　a　g-Riesz　basis　in　a　complex　Banach　space.　We　also　give　a　result　about　the　stability　of　g-frame　in　a　complex　Banach　space.　©　2010　World　Scientific　Publishing　Company.