  $Z^\prime$ boson as a new gauge boson has been proposed in many new physics
models. The interactions of $Z^\prime$ coupling to fermions are detailed
studied at the large hadron collider. A $Z^\prime$ with the mass of a few TeV
has been excluded in some special models. The future lepton colliders will
focus on the studies of Higgs physics which provide the advantage to
investigate the interactions of Higgs boson with the new gauge bosons. We
investigate the $Z^\prime ZH$ interaction via the process of $e^+e^- \to
Z^\prime/Z \to ZH \to l^+l^- b \bar{b}$. The angular distribution of the final
leptons decaying from the $Z$-boson is related to the mixing of $Z^\prime$-$Z$
and the mass of $Z^\prime$. The forward-backward asymmetry has been proposed as
an observable to investigate the $Z^\prime$-$Z$ mixing. The angular
distributions change significantly with some special beam polarization
comparing to the unpolarized condition.
