  We study a Zee model applying a modular $A_4$ symmetry, where we construct
our lepton model as minimum modular weight as possible. We show our predictions
on phases and neutrino masses through our $\Delta \chi^2$ analysis. We find
that normal hierarchy is favored, and $\tau$ is localized to 2.3$i$ that is
close to a fixed point of $i\times \infty$. In this limit, our neutrino mass
matrix comes to a two zero texture, which is called $B_1$ of the neutrino mass
matrix. We show that our phase predictions are in good agreement with the ones
of $B_1$.
