  The implications of the family non-universal $Z^\prime$ model in the $B\to
K_{1}(1270,1400)\ell^{+}\ell^{-}(\ell=e\,,\mu\,,\tau)$ decays are explored,
where the mass eigenstates $K_{1}(1270,1400)$ are the mixtures of $^{1}{P}_{1}$
and $^{3}{P}_{1}$ states with the mixing angle $\theta$. In this work,
considering the $Z^\prime$ boson and setting the mixing angle
$\theta=(-34\pm13)^{\circ}$, we analyze the branching ratio, the dilepton
invariant mass spectrum, the normalized forward-backward asymmetry and lepton
polarization asymmetries of each decay mode. We find that all observables of
$B\to K_{1}(1270)\mu^{+}\mu^{-}$ are sensitive to the $Z^{\prime}$
contribution. Moreover, the observables of $B\to K_{1}(1400)\mu^{+}\mu^{-}$ are
relatively strong $\theta$-dependence; thus, the $Z^{\prime}$ contribution will
be buried by the uncertainty of the mixing angle $\theta$. Furthermore, the
zero crossing position in the FBA spectrum of $B\to K_{1}(1270)\mu^{+}\mu^{-}$
at low dilepton mass will move to the positive direction with $Z^\prime$
contribution. For the tau modes, the effects of $Z^\prime$ are not remarkable
due to the small phase space. These results could be tested in the running
LHC-b experiment and Super-B factory.
