  We propose a simple gauged U(1)$_{B-L}$ extension of the minimal
supersymmetric Standard Model (MSSM), where R-parity is conserved as usual in
the MSSM. The global $B-L$ (baryon number minus lepton number) symmetry in the
MSSM is gauged and three MSSM gauge-singlet chiral multiplets with a unit $B-L$
charge are introduced, ensuring the model free from gauge and gravitational
anomalies. We assign an odd R-parity for two of the new chiral multiplets and
hence they are identified with the right-handed neutrino superfields, while an
even R-parity is assigned to the other one ($\Phi$). The scalar component of
$\Phi$ plays the role of a Higgs field to break the U(1)$_{B-L}$ symmetry
through its negative mass squared, which is radiatively generated by the
renormalization group running of soft supersymmetry (SUSY) breaking parameters
from a high energy. This radiative U(1)$_{B-L}$ symmetry breaking leads to its
breaking scale being at the TeV naturally. Because of our novel R-parity
assignment, three light neutrinos are Dirac particles with one massless state.
Since R-parity is conserved, the lightest neutralino is a prime candidate of
the dark matter as usual. In our model, the lightest eigenstate of the mixture
of the $B-L$ gaugino and the fermionic component of $\Phi$ appears as a new
dark matter candidate. We investigate phenomenology of this dark matter
particle. We also discuss collider phenomenology of our model. In particular,
the $B-L$ gauge boson ($Z'$), once discovered at the Large Hadron Collider, can
be a probe to determine the number of (right-handed) Dirac neutrinos with its
invisible decay width, in sharp contrast with the conventional $B-L$ extension
of the SM or MSSM where the right-handed neutrinos are heavy Majorana particles
and decay to the SM leptons.
