  Motivated by the large discrepancy of CP-violating phase in $\bar{B}_s-B_s$
mixing between the experimental data and the Standard Model prediction, we
pursue possible solutions within a family non-universal $Z^{\prime}$ model.
Within such a specific model, we find that both the $\bar{B}_s-B_s$ mixing
anomaly and the well-known "$\pi K$ puzzle" could be moderated simultaneously
with a nontrivial new weak phase, $\phi^L_s\sim-72^{\circ}$ (S1) or
$-82^{\circ}$ (S2). With the stringently constrained $Z^{\prime}$ coupling
$B_{sb}^{L}$, we then study the $Z^{\prime}$ effects on the rare $B\to X_s
\mu^+\mu^-$ and $B_s\to \mu^+\mu^-$ decays, which are also induced by the same
$b\to s$ transition. The observables of $B\to X_s \mu^+\mu^-$, at both high and
low $q^2$ regions, are found to be able to put strong constraints on the
$\mu-\mu-Z^{\prime}$ coupling, $B_{\mu\mu}^{L,R}\sim10^{-2}$. It is also shown
that the combined constraints from $\bar{B}_s-B_s$ mixing, $B\to \pi K$ and
$B\to X_s \mu^+\mu^-$ do not allow a large $Z^{\prime}$ contribution to the
pure leptonic $B_s\to\mu^+\mu^-$ decay.
