  We discuss type-II seesaw models adopting modular $A_4$ symmetry in
supersymmetric framework. In our approach, the models are classified by the
assignment of $A_4$ representations and modular weights for leptons and triplet
Higgs fields. Then neutrino mass matrix is characterized by modulus $\tau$ and
two free parameters. Carrying out numerical analysis, we find allowed parameter
sets which can fit the neutrino oscillation data. For the allowed parameter
sets, we obtain the predictions in neutrino sector such as CP violating phases
and the lightest neutrino mass. Finally we also show the predictions for the
branching ratios of doubly charged scalar boson focusing on the case where the
doubly charged scalar boson dominantly decays into charged leptons.
