We explore the generalized Drazin inverse in a Banach algebra. Let A be a Banach algebra, and let a, b ∈ A d. If ab = λa π bab π for a nonzero complex number λ, then a + b ∈ A d. The explicit representation of (a + b) d is presented. As applications of our results, we present new representations for the generalized Drazin inverse of a block matrix in a Banach algebra. The main results of Liu and Qin [Representations for the generalized Drazin inverse of the sum in a Banach algebra and its application for some operator matrices, Sci. World J., 2015, 156934.8] are extended