  We construct a model to explain the muon anomalous magnetic moment, without
considering any lepton flavor violations, in the modular $A_4$ symmetry. We
have investigated a predictive radiative seesaw model including dark matter
candidate at favorable fixed point of $\tau=\omega$ obtained by recent analysis
of the stabilized moduli values from the possible configurations of the flux
compactifications. In the result, we show our predictions on the Dirac CP and
Majorana phases, the neutrino masses, the mass range of dark matter as well as
the muon anomalous magnetic moment through the $\chi^2$ analysis.
