  One-loop $W$ boson contributions to the decay $H\rightarrow Z\gamma$ in the
general $R_\xi$ gauge are presented. The analytical results are expressed in
terms of well-known Passarino-Veltman functions which their numerical
evaluations can be generated using {\tt LoopTools}. In the limit $d\rightarrow
4$, we have shown that these analytical results are independent of the
unphysical parameter $\xi$ and consistent with previous results. The gauge
parameter independence are also checked numerically for consistence. Our
results are also well stable with different values of $\xi =0, 1, 100,$ and
$\xi \rightarrow \infty$.
