For A ∈ L(X), B ∈ L(Y) and C ∈ L(Y,X) we denote by MC the operator matrix defined on X ⊕ Y by MC = ( A C 0 B ) . In this paper, we prove that σqF(A) ∪ σqF(B) ⊊ ⋃ C∈L(Y,X) σqF(MC) ∪ σp(B) ∪ σp(A∗), where σqF(.) (resp. σp(.)) denotes the quasi-Fredholm spectrum (resp. the point spectrum). Furthermore, we consider some sufficient conditions for MC to be quasi-Fredholm and sufficient conditions to have σqF(A) ∪ σqF(B) = ⋂ C∈L(Y,X) σqF(MC).