  $B_q^0-B_^0 bar$ mixing offers a profound probe into the effects of new
physics beyond the Standard Model. In this paper, $B_s^0-B_s^0 bar$ and
$B_d^0-B_d^0 bar$ mass differences are considered taking the effect of both
Z-and Z' -mediated flavour-changing neutral currents in the $B_q^0-B_q^0 bar$
mixing (q = d, s). Our estimated mass of Z' boson is accessible at the
experiments LHC and B-factories in near future.
