  The exclusive decay of the Higgs boson to a vector meson ($ J/\psi $ or $
\Upsilon(1S) $) and $ Z $ boson is studied in this work. The decay amplitudes
are separated into two parts in a gauge invariant manner. The first part comes
from the direct coupling of the Higgs boson to the charm (bottom) quark and the
other from the $ HZZ^{*} $ or the loop-induced $ HZ\gamma^{*} $ vertexes in the
standard model. While the branching ratios from the direct channel are much
smaller than those of the indirect channel, their interference terms give
nontrivial contributions. We further calculate the QCD radiative corrections to
both channels, which reduce the total branching ratios by around 20% for both $
J/\psi $ and $ \Upsilon(1S) $ production. These results may help to check the
SM predictions of the $ H c\bar{c}(H b\bar{b}) $ coupling and to seek for hints
of new physics at the High Luminosity LHC or future hadron colliders.
