  We construct a new gauged $U(1)_\ell$ lepton number model which is
anomaly-free for each SM generation. The active neutrino masses are radiatively
generated with a minimal scalar sector. The phenomenology and collider signals
are studied. The interference effects among the new gauge boson, $Z_\ell$,
photon, and $Z$-boson can be probed at the future $e^+e^-$ colliders even if
the center-of-mass energy is below the mass of $Z_\ell$. Moreover, the
electroweak precision sets a stringent bound on the mass splitting of the new
lepton doublets.
