  It is pointed out that there exist a few problems to be overcome toward an
observable sub-eV QCD axion in superstring compactification. We give a general
expression for the axion decay constant. For a large domain wall number
$N_{DW}$, the axion decay constant can be substantially lowered from a generic
value of a scalar singlet VEV. The Yukawa coupling structure in the recent
$Z_{12-I}$ model is studied completely, including the needed nonrenormalizable
terms toward realistic quark and lepton masses. In this model we find an
approximate global symmetry and vacuum so that a QCD axion results but its
decay constant is at the GUT scale. The axion-photon-photon coupling is
calculated for a realistic vacuum satisfying the quark and lepton mass matrix
conditions. It is the first time calculation of $c_{a\gamma\gamma}$ in
realistic string compactifications: $c_{a\gamma\gamma}={5/3}-1.93\simeq -0.26$.
