  We investigate the process $pp \rightarrow HZ\gamma + X$ at the
$\sqrt{s}=14~{\rm TeV}$ LHC up to the QCD next-to-leading order (NLO), and
discuss the kinematic distributions of final products after on-shell Higgs and
$Z$-boson decays by adopting the narrow width approximation. The dependence of
the leading order (LO) and the QCD NLO corrected integrated cross sections on
the factorization/renormalization scale is studied. Our results show that the
LO integrated cross section and kinematic distributions are significantly
enhanced by the NLO QCD corrections, and the NLO QCD $K$-factor strongly
depends on the observables and phase space. We conclude that in precision
experimental data analyse for probing the $HZ\gamma$ coupling we should
consider the NLO QCD corrections and put proper constraints on lepton-pair
invariant mass to reduce the background.
