  We propose a simple setup which can stabilize a modulus field of the finite
modular symmetry by the Coleman-Weinberg potential. Our scenario leads to a
large hierarchy suppressing instanton-like corrections $e^{2\pi i\tau}$ and to
a light axion identified as $\mathrm{Re} \tau$, where $\tau$ is the modulus
field. This stabilization mechanism provides the axion solution to the strong
CP problem. The potential has a minimum at a large $\mathrm{Im}\tau$ which
suppresses explicit $U(1)_{\mathrm{PQ}}$ violation terms proportional to
$e^{-2\pi {\mathrm{Im}\tau}}$, and hence the quality of the axion is ensured by
the residual symmetry associated with the $T$-transformation, $\tau \to \tau
+1$, around the fixed point $\tau \sim i\infty$.
