  We search for predictability of lepton masses and mixing patterns of type-II
seesaw scenario in a non-holomorphic modular $A_4$ symmetry recently proposed
by "Qu" and "Ding". We propose three types of minimum predictive models with
different assignments of modular weight, satisfying the neutrino oscillation
data in Nufit 5.2. The cosmological bound on the sum of neutrino mass is
stringent to our models and CMB bound $\sum D_\nu\le0.12$ eV can be satisfied
by one of three models playing an important role in discriminating them.
