  We study a successful model to explain the muon anomalous magnetic moment
originating from Yukawa-type interactions {in a supersymmetric theory}. Thanks
to a modular $A_4$ flavor symmetry, any lepton flavor violations that spoil the
model are forbidden. We also investigate a predictive radiative seesaw model
including a dark matter (DM) candidate. At first, we construct the minimum
model to satisfy the neutrino oscillation data and obtain several predictions
such as Dirac CP and Majorana phases, the neutrino masses through $\chi^2$
analysis. However, the minimum model would not provide our promising DM
candidate. Thus, we minimally extend the model and find a good DM candidate. In
the extended framework, we show the allowed regions to satisfy the muon
anomalous magnetic moment and the observed relic density of dark matter in
addition to predictions of the lepton sector.
