Using the form factors calculated in the three-point QCD sum rules, we calculate the new physics contributions to the physical observables of Bc → D * s µ + µ − decay in a family non-universal Z ′ model. Under the consideration of three cases of the new physics parameters, we find that: (a) the Z ′ boson can provide large contributions to the differential decay rates; (b) the forward-backward asymmetry (FBA) can be increased by about 47%, 38%, and 110% at most in S1, S2, and extreme limit values (ELV), respectively. In addition, the zero crossing can be shifted in all the cases; (c) when ŝ > 0.08, the value of PL can be changed from −1 in the Standard Model (SM) to −0.5 in S1, −0.6 in S2, and 0 in extreme limit values, respectively; (d) the new physics corrections to PT will decrease the SM prediction about 25% for the cases of S1 and S2, 100% for the case of ELV.