We present necessary and sufficient conditions under which the anti-triangular matrix a b 1 0 over a Banach algebra has g-Drazin inverse. New additive results for g-Drazin inverse are obtained. Then we apply our results to 2 × 2 operator matrices and generalize many known results, e.g., [5, Theorem 2.2], [13, Theorem 2.1] and [14, Theorem 4.1].