We present new conditions under which Cline's formula and Jacobson's lemma for g-Drazin inverse hold. Let A be a Banach algebra, and let a, b ∈ A satisfying a k b k a k = a k+1 for some k ∈ N. We prove that a has g-Drazin inverse if and only if b k a k has g-Drazin inverse. In this case, (b k a k) d = b k (a d) 2 a k and a d = a k [(b k a k) d ] k+1. Further, we study Jacobson's lemma for g-Drazin inverse in a Banach algebra under the preceding condition. The common spectral property of bounded linear operators on a Banach space is thereby obtained