We study the effects of an extra U(1)' gauge boson with flavor changing couplings with fermion mass eigenstates on certain B meson decays that are sensitive to such new physics contributions. In particular, we examine to what extent the current data on Bd --> phiK and Bd --> eta'K decays may be explained in such models, concentrating on the example in which the flavor changing couplings are left-chiral. We find that within reasonable ranges of parameters, the Z' contribution can readily account for the anomaly in S-phiKs but is not sufficient to explain large branching ratio of Bd --> eta'K with the same parameter value. S-phiKs and S-eta'Ks are seen to be the dominant observables that constrain the extra weak phase in the model. (C) 2003 Published by Elsevier B.V.