We revisit B̅_s→π K, π K^∗ and ρ K decays within QCDF formalism and examine the possible effects of a family non-universal Z^' boson in these decays. In our evaluations, the strong constraints from B_d-B̅_̅d̅ mixing on the strength of the left-handed flavor-changing d-b-Z^' coupling B_db^L (∼0.2×10^-3) is also included. Numerically, we find that a new weak phase ϕ^L_d∼-50^∘ involved in B_db^L, the negative combination of the u-u-Z^' and d-d-Z^' couplings P_ud^R and/or D_ud^L with larger

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... value are crucial to improve the agreement of B(B̅_s→π^- K^+) between the SM prediction and the experimental measurement. Generally, B(B̅_s→π^- K^+) could be reduced by about 18 most by Z^' contributions. Moreover, combining with the recent updated measurement on β_s by CDF and D0 collaborations, we also find that Z^' effects in B̅_s→π^- K^+ decays are very important for examining whether the CKM-like hierarchy persists in a family non-universal Z^' coupling matrix.