  We study the Zee-Babu two-loop neutrino mass generation model and look for a
possible flavor symmetry behind the tri-bimaximal neutrino mixing. We find that
there probably exists the mu-tau symmetry in the case of the normal neutrino
mass hierarchy, whereas there may not be in the inverted hierarchy case. We
also propose a specific model based on a Froggatt-Nielsen-like $Z_5$ symmetry
to naturally accomplish the mu-tau symmetry on the neutrino mass matrix for the
normal hierarchy case.
