  We propose a model with $U(1)_{B-L}$ gauge symmetry and several new fermions
in no conflict with anomaly cancellation where the neutrino masses are given by
the vacuum expectation value of Higgs triplet induced at the one-loop level.
The new fermions are odd under discrete $Z_2$ symmetry and the lightest one
becomes dark matter candidate. We find that the mass of dark matter is
typically $O(1)$-$O(10)$ GeV. Then relic density of the dark matter is
discussed.
