  We have investigated $B \to (K,K^*)(l\bar l,\nu\bar\nu)$ decay channels and
predicted some form factor dependent observables (e.g. branching ratio,
forward-backward asymmetry and lepton polarization asymmetry) considering new
physics contribution from non-universal $Z'$ model. We have found that there is
appreciable difference between the standard model and $Z'$ model predictions.
Recently, the lepton flavour non-universality parameters $R_K$ and $R_{K^*}$
have been measured by the LHCb collaboration and are found to be different from
their standard model predictions. These deviations provide the hint of flavor
non-universality in lepton sector and motivate our research to look for new
physics beyond the standard model. The $R_K$ and $R_{K^*}$ anomalies may be due
to new physics in either electron or muon sector or both. In our work, we have
shown that the experimental results of $R_K$ and $R_{K^*}$ could be achieved in
non-universal $Z'$ model considering the new physics couplings to muon sector
only.
