An element a in a Banach algebra A has p-Drazin inverse provided that there exists b ∈ comm(a) such that b = b 2 a, a k − a k+1 b ∈ J(A) for some k ∈ N. In this paper, we present new conditions for a block operator matrix to have p-Drazin inverse. As applications, we prove the p-Drazin invertibility of the block operator matrix under certain spectral conditions