  We study a simple extension of the Zee model, in which a discrete $Z_2$
symmetry imposed in the original model is replaced by a global $U(1)$ symmetry
retaining the same particle content. Due to the $U(1)$ symmetry with flavor
dependent charge assignments, the lepton sector has an additional source of
flavor violating Yukawa interactions with a controllable structure, while the
quark sector does not at tree level. We show that current neutrino oscillation
data can be explained under constraints from lepton flavor violating decays of
charged leptons in a successful charge assignment of the $U(1)$ symmetry. In
such scenario, we find a characteristic pattern of lepton flavor violating
decays of additional Higgs bosons, which can be a smoking gun signature at
collider experiments.
