Motivated by the latest improved measurements of B-meson decays, we make a comprehensive analysis of the impact of a family non-universal Z' boson on B-s - (B) over bar (s) mixing and two-body hadronic B-meson decays, all being characterized by the quark-level b -> s transition. Explicitly 22 decay modes and the related 52 observables are considered, and some interesting correlations between them are also carefully examined. Firstly, the allowed oases of b - s - Z' coupling parameters |B-sb(L, R)| and phi(L, R)(s) are extracted from B-s - (B) over bar (s) mixing. Then, in the 'SM limit' (i.e.,...