  We consider a supergravity model that has the modular $A_4$ symmetry and
discuss the interplay between the neutrino mixing and inflation. The model
contains right-handed neutrinos that have the Majorana masses and additional
Yukawa couplings to the waterfall field. In the model an active neutrino is
massless and we find that only the inverted hierarchy is allowed and the
Majorana phase is predicted to be around $\pm (120\text{--}180)^\circ$ from the
observed neutrino mixing data. In the early universe, one of right-handed
sneutrinos plays the role of the inflaton field. Focusing on the subcritical
regime of the hybrid inflation that is consistent with the cosmic microwave
background data, we analyze the dynamics of the scalar sector and derive an
upper bound $\mathcal{O}(10^{10})~{\rm GeV}$ on the scale of the Majorana mass.
