Let A be a complex Banach algebra. An element a ∈ A has g-Drazin inverse if there exists b ∈ A such that b = bab, ab = ba, a − a 2 b ∈ A qnil. Let a, b ∈ A d. If a 3 b = ba, b 3 a = ab, and a 2 a d b = aa d ba, we prove that a + b ∈ A d if and only if 1 + a d b ∈ A d. We present explicit formula for (a + b) d under certain perturbations. These extend the main results of Wang, Zhou and Chen (Filomat, 30(2016), 1185–1193) and Liu, Xu and Yu (Applied Math. Comput., 216(2010), 3652–3661).