  We study the $B-L$ gauge extension of the Standard Model which contains a
singlet scalar and three right-handed neutrinos. The vacuum expectation value
of the singlet scalar breaks the $U(1)_{B-L}$ symmetry. Here the third
generation right-handed neutrino is qualified as the dark matter candidate, as
an artifact of $Z_2$-charge assignment. Relic abundance of the dark matter is
consistent with WMAP9 and PLANCK data, only near scalar resonances where dark
matter mass is almost half of the scalar boson masses. Requiring correct relic
abundance, we restrict the parameter space of the scalar mixing angle and mass
of the heavy scalar boson of this model. Besides this, the maximum value of
spin-independent scattering cross-section off nucleon is well-below the {\sc
Xenon100} and recent LUX exclusion limits and can be probed by future {\sc
Xenon1T} experiment. In addition, we compute the annihilation of the dark
matter into two photon final state in detail and compare with the Fermi-LAT
upper bound on $\langle\sigma v\rangle_{\gamma \gamma}$ for NFW and Einasto
profile.
