We study the $B-L$ gauge extension of the Standard Model which contains a singlet scalar and three right-handed neutrinos. 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. Requiring correct relic abundance, we restrict the parameter space of the scalar mixing angle and mass of the heavy scalar boson of this model.