  We propose a supersymmetric extension of the minimal $B-L$ model where we
consider a new $Z_2$-parity under which one right-handed neutrino is assigned
odd parity. When the Majorana Yukawa coupling of a $Z_2$-even right-handed
neutrino is large, radiative corrections will drive the mass squared of the
corresponding right-handed sneutrino to negative values, breaking the $B-L$
gauge symmetry at the TeV scale in a natural way. Additionally, R-parity is
broken and thus the conventional supersymmetric dark matter candidate, the
neutralino, is no longer viable. Thanks to the $Z_2$-parity, the $Z_2$-odd
right-handed neutrino remains a stable dark matter candidate even in the
presence of R-parity violation. We demonstrate that the dark matter relic
abundance with an enhanced annihilation cross section by the $B-L$ gauge boson
(Z') resonance is in accord with the current observations. Therefore, it
follows that the mass of this dark matter particle is close to half of the Z'
boson mass. If the Z' boson is discovered at the Large Hadron Collider, it will
give rise to novel probes of dark matter: The observed Z' boson mass will
delineate a narrow range of allowed dark matter mass. If the Z' boson decays to
a pair of dark matter particles, a precise measurement of the invisible decay
width can reveal the existence of the dark matter particle.
