  We present one-loop formulas for contributing to the $HZZ$ vertex in 't
Hooft-Veltman gauge within Standard Model framework. One-loop off-shell Higgs
decay rates to $Z$-pair are investigated in both unpolarized and longitudinal
polarization for $Z$ bosons in final state. The corrections are range of $7\%$
to $8.4\%$ when we vary the off-shell Higgs mass from $200$ GeV to $500$ GeV.
In applications, we study off-shell Higgs decay $H^* \rightarrow ZZ$ in the
Higgs productions at future colliders such as the signal processes
$\gamma^*(Q^2)\gamma \rightarrow H^* \rightarrow ZZ$ and $e^-\gamma \rightarrow
e^-H^* \rightarrow e^- ZZ$ are analyzed.
