  We study a two-loop finiteness of an effective potential for a Higgs boson
that is the fifth component of a gauge field in an $U(1)$ gauge theory coupled
to quantum gravity on the five-dimensional space-time $M^4\times S^1$. There
are two types of diagrams including quantum gravitational corrections. We find
that only one type of diagram contributes to the effective potential for the
Higgs boson in fact and its magnitude is finite.
