In this paper, we study additive properties of the generalized Drazin inverse in a Banach algebra. We first show that a + b ∈ A d under the condition that a, b ∈ A d , aba π = λa π bab π a π , and then give some explicit expressions for the generalized Drazin inverse of the sum a + b under some weaker conditions than those used in the previous papers. Some known results are extended.