Motivated by the very recent measurements performed at the LHCb and the Tevatron of the B 0 s −B 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 likesign 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 s 12 , it is found that, once the combined constraints from ∆M s , φ s and ∆Γ s are imposed, the model could not explain the measured flavour-specific CP asymmetry a s f s , at least within its 1σ ranges. In the second scenario where the NP contributes also to the absorptive part Γ s 12 via tree-level Z -induced b → ccs operators, we find that, with the constraints from ∆M s , φ s and the indirect CP asymmetry inB d → J/ψK S taken into account, the present measured 1σ experimental ranges for a s f 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 0 s −B 0 s 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.