Abstract: Motivated by the very recent measurements performed at the LHCb and the Tevatron of the B-s(0) – (B) over bar (0)(s) mixing, in this paper we revisit it in a family non-universal Z' model, to check if a simultaneous explanation for all the mixing observables, especially for the like-sign dimuon charge asymmetry observed by the D0 collaboration, could be made in such a specific model. In the first scenario where the Z' boson contributes only to the off-diagonal element M-12(s), it is found that, once the combined constraints from Delta M-s, phi(s) and Delta Gamma(s) are imposed, the model could not explain the measured flavour-specific CP asymmetry a(fs)(s), at least within its 1 sigma ranges. In the second scenario where the NP contributes also to the absorptive part Gamma(s)(12) via tree-level Z'-induced b -> c (c) over bars operators, we find that, with the constraints from Delta M-s, phi(s) and the indirect CP asymmetry in (B) over bar (d) -> J/psi K-S taken into account, the present measured 1 sigma experimental ranges for a(fs)(s) could not be reproduced too. Thus, such a specific Z' model with our specific assumptions could not simultaneously reconcile all the present data on B-s(0) – B-s(0) mixing. Future improved measurements from the LHCb and the proposed superB experiments, especially of the flavour-specific CP asymmetries, are expected to shed light on the issue.