The Duffin-Kemmer-Petiau (DKP) equation is solved approximately for a vector exponential-like decaying potential with any arbitrary J -state by using the Pekeris approximation. The generalized parametric Nikiforov-Uvarov (NU) method is used to obtain energy eigenvalues and corresponding wave functions in a closed form. The cases of zero total angular momentum and nonrelativistic limit are discussed too.