  We study a quasi two-zero neutrino texture based on type-II seesaw model in a
modular $A_4$ symmetry to evade the cosmological bound on the sum of neutrino
mass while keeping some predictability in neutrino sector. Working on three
fixed points for modulus, we discuss predictions of the model and show the
allowed points satisfying the cosmological bound on neutrino mass from both CMB
and CMB+BAO data.
