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 $c_{agammagamma}$ in realistic string compactifications: $c_{agammagamma}={5/3}-1.93simeq -0.26$.
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