Motivated by the measured large branching ratio of (the so-called ππ puzzle), we investigate the effects of a family nonuniversal Z′ model on the tree-dominated B → ππ decays. We find that the Z′ coupling parameter with a nontrivial new weak phase , which is relevant to the Z′ contributions to the QCD penguin sector △C5, is needed to reconcile the observed discrepancy. Combined with the recent fitting results from B → πK, πK* and ρK decays, the Z′ parameter spaces are severely reduced but still not excluded entirely, implying that...