Let A be a Banach algebra. An element a ∈ A has the generalized Zhou inverse if there exists b ∈ A such that b = bab, ab = ba, a n − ab ∈ J # (A), f or some n ∈ N. We find some new conditions under which the generalized Zhou inverse of the sum a + b can be explicitly expressed in terms of a, b, a z , b z. In particular, necessary and sufficient conditions for the existence of the generalized Zhou inverse of the sum a + b are obtained.