  A new model for tiny neutrino masses is proposed in the gauge theory of
$SU(3)_C \otimes SU(3)_L \otimes U(1)_X$, where neutrino masses are generated
via the quantum effect of new particles. In this model, the fermion content is
taken to be minimal to realize the gauge anomaly cancellation, while the scalar
sector is extended from the minimal 3-3-1 model to have an additional $SU(3)_L$
triplet field. After $SU(3)_L\otimes U(1)_X$ is broken into $SU(2)_L\otimes
U(1)_Y$, the "Zee model" like diagrams are naturally induced, which contain
sufficient lepton flavor violating interactions to reproduce current neutrino
oscillation data. Furthermore, the remnant $Z_2$ symmetry appears after the
electroweak symmetry breaking, which guarantees the stability of dark matter.
It is confirmed that this model can satisfy current dark matter data. As an
important prediction to test this model, productions and decays of
doubly-charged scalar bosons at collider experiments are discussed in
successful benchmark scenarios.
