  We present a minimal extension of the left-right symmetric model based on the
gauge group $SU(3)_{c} \times SU(2)_{L} \times SU(2)_{R} \times U(1)_{B-L}
\times U(1)_{X}$, in which a vector-like fermion pair ($\zeta_L$ and $\zeta_R$)
charged under the $U(1)_{B-L} \times U(1)_X$ symmetry is introduced. Associated
with the symmetry breaking of the gauge group $SU(2)_{R} \times U(1)_{B-L}
\times U(1)_{X}$ down to the Standard Model (SM) hypercharge $U(1)_Y$, Majorana
masses for $\zeta_{L, R}$ are generated and the lightest mass eigenstate plays
a role of the dark matter (DM) in our universe by its communication with the SM
particles through a new neutral gauge boson "$X$". We consider various
phenomenological constraints of this DM scenario, such as the observed DM relic
density, the LHC Run-2 constraints from the search for a narrow resonance, and
the perturbativity of the gauge couplings below the Planck scale. Combining all
constraints, we identify the allowed parameter region which turns out to be
very narrow. A significant portion of the currently allowed parameter region
will be tested by the High-Luminosity LHC experiments.
