  We studied the isotope effect of phonon in the Fe-based superconductors using
a phenomenological two band model for the sign-changing s-wave ($\pm$s-wave)
state. Within this mean-field model, we showed that the large isotope effect is
not inconsistent with the $\pm$s-wave pairing state and its high transition
temperature. In principle, a large phonon isotope coefficient $\alpha$ implies
a large phonon coupling constant. However, the asymmetric density of states
(DOS) between two bands substantially enhances the value of $\alpha$, so that a
moderate value of the phonon coupling constant ($\lambda_{\rm ph} \approx 0.4$)
can produce a very large value of $\alpha$ ($\approx 0.4$) as well as a high
transition temperature together with an antiferromagnet (AFM)-induced
interaction.
