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We study the impacts of nonuniversal $Z^{\prime}$ model, providing flavorchanging neutral current at tree level, on the branching ratios (BRs), CPasymmetries (CPAs) and polarization fractions of B decays. We find that forsatisfying the current data, the new left- and right-handed couplings have tobe included at the same time. The new introduced effective interactions notonly could effectively explain the puzzle of small longitudinal polarization in$B\to K^* \phi$ decays, but also provide a solution to the small CPA of$B^{\pm}\to \pi^{0} K^{\pm}$. We also find that the favorable CPA of$B^{\pm}\to \pi^{0} K^{\pm}$ is opposite in sign to the standard model;meanwhile, the CPA of $B_{d}\to \pi^{0}K$ has to be smaller than -10%. Inaddition, by using the values of parameters which are constrained by $B\to \piK$, we find that the favorable ranges of BRs, CPAs, longitudinal polarizations,and perpendicular transverse polarizations for $(B^{\pm}\to \rho^{\pm} K^{*},B_{d}\to \rho^{\mp} K^{*\pm})$ are $(17.1\pm 3.9, 10.0\pm2.0)\times 10^{-6}$,$(3\pm 5, 21\pm 7)%$, $(0.66\pm 0.10, 0.44\pm 0.08)$ and $(0.14\pm 0.10,0.25\pm 0.09)$, respectively.Comment: 28 pages, 9 figures, version revise

physical review. d. particles, fields, gravitation, and cosmology/physical review. d, particles, fields, gravitation, and cosmology

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