  Based on the Peccei-Quinn (PQ) assignment, the PQ charge operator in the
3-3-1 model with Cosmological Inflation is constructed in terms of diagonal
generators $T_3$ and $T_8$ of the $SU(3)_L$ subgroup. The formula shows that
difference of PQ charges of up and down quarks is 2, i.e., $\De Q_A =2$, while
for electric charge, are assumed to be equal, while the ($Q_A$) are opposite.
PQ charge of neutral scalars equal $\pm 2$, while for charged scalars, it
vanishes. The couplings of axion with fermions are presented. To have correct
kinetic term for the axion, the PQ scale $f_{a}$ is to be VEV of the singlet
scalar boson, namely, $f_{a}= v_\phi$. The photon couples to charged particles
only, while in this model, the axion does not couple to charged scalar/gauge
bosons. The point is worth emphasizing that the axion has doubly derivative
coupling with scalar playing the role of inflaton. The new effects mainly
happen in the energy region from $10^7 \, \gev$ to $10^{11} \, GeV$. The chiral
effective Lagrangian as usually provides axion mass consistent with
model-independent prediction.
