  We study one-loop quantum gravity corrections to the standard model Higgs
potential $V(\phi)$ $\grave{\rm a}$ la Coleman-Weinberg and examine the
stability question of $V(\phi)$ in the energy region of Planck mass scale,
$\mu\simeq M_{\rm Pl}$ ($M_{\rm Pl}=1.22\times10^{19}{\rm GeV}$). We calculate
the gravity one-loop corrections to $V(\phi)$ in Einstein gravity by using the
momentum cut-off $\Lambda$. We have found that even small gravity corrections
compete with the standard model term of $V(\phi)$ and affect the stability
argument of the latter part alone. This is because the latter part is nearly
zero in the energy region of $M_{\rm Pl}$.
