The zero mode of an extra-dimensional component of gauge potentials serves as a 4D Higgs field in the gauge-Higgs unification. We examine QED on $M^4 times S^1$ and determine the mass and potential of a 4D Higgs field (the $A_5$ component) at the two
loop level with gauge invariant reguralization. It is seen that the mass is free from divergences and independent of the renormalization scheme.
