  We provide a minimal alternative gauged U(1)$_{\rm B-L}$ model in which three
right-handed neutrinos with charges of (5,-4,-4) and only one B-L Higgs field
with charge 1 are introduced. Consistent active neutrino masses and mixings can
be obtained if the $Z_2$ symmetry on two of the right-handed neutrinos is
introduced. It predicts two heavy degenerate right-handed neutrinos, which may
realize resonant leptogenesis scenario, and one relatively light sterile
neutrino, which is a good dark matter candidate.
