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 $SU(3)_Lotimes U(1)_X$ is broken into $SU(2)_Lotimes U(1)_Y$, 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.
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