The decay modes (B) over bar (s) -> pi(0)(rho(0)) eta(') are dominated by electroweak penguins that are small in the standard model. In this work we investigate the contributions to these penguins from a model with an additional U(1)' gauge symmetry and show there effects on the branching ratios of (B) over bar (s) -> pi(0)(rho(0)) eta((')). In a scenario of the model, where Z' couplings to the left-handed quarks vanish, we show that the maximum enhancement occurs in the branching ratio of (B) over bar (0)(s) -> pi(0) eta' where it can reach 6 times the SM prediction. On the other hand, in a scenario of the model where Z' couplings to both left-handed and righthanded quarks do not vanish, we find that Z' contributions can enhance the branching ratio of B-s(0) -> rho(0) eta up to one order of magnitude comparing to the SM prediction for several sets of the parameter space where both Delta M-Bs and S-psi phi constraints are satisfied. This kind of enhancement occurs for a rather fine-tuned point where the Delta M-Bs constraint on | S-SM(B-s) + S-Z' (B-s) | is fulfilled by overcompensating the SM via S-Z' (B-s) similar or equal to -2S(SM)(B-s).