  We study a Zee-Babu model in a modular $A_4$ flavor symmetry, in which we
search for several predictions such as phases, sum of neutrino masses, and
neutrinoless double beta decay, satisfying neutrino oscillation data in a
minimum framework of the charge assignments of modular weight. We perform
$\Delta \chi^2$ analysis to get our results and find $\tau$ is localized nearby
at one of the fixed points of $i\times \infty$ for both of normal and inverted
mass hierarchies.
