Motivated by recent measurements of the neutral Bs-meson mixing, obtained by LHCb group and the Tevatron, and the possibility to have sizable NP effects in 12s, we revisit the Bs mixing in a family non-universal Z' model. We assume that the Z' boson contributes to the off-diagonal element M12s and also to the off-diagonal element 12s via tree-level Z'-induced b scc operators. We find that, with the constraints from Mss and the indirect CP asymmetry in BdJ/KS imposed, the present measured 1 experimental ranges for afss could not be reproduced. Thus, such a specific model could not simultaneously explain the present data on Bs mixing. It is expected that with the operation of the LHCb group and the future super B experiments, more accurate measurements, especially of the flavour-specific CP asymmetries, could shed light on the issue.