Fig. 1 shows the relic density Ω$_{N}$ h 2 as a function of the DM mass m$_{N}$ for a set of parameters: ( v ′ , M$_{h}$, M$_{H}$, M$_{Z}$ ′ , sin θ ) = (4000 GeV , 120 GeV , 200 GeV , 1000 GeV , 0 . 7), for example. Willkinson Microwave Anisotropy Probe measured the value of DM abundance as Ω$_{DM}$ h 2 ≃ 0 . 1 [15]. The figure shows that a desired DM relic abundance can be obtained for only near Higgs resonances, m$_{N}$ ≈ M$_{h}$/ 2 or M$_{H}$/ 2. Fig. 2 shows the relic density Ω$_{N}$ h 2 as a function of the DM mass m$_{N}$ for a smaller Higgs mixing sin θ = 0 . 3 (others are the same as in Fig. 1). Compared with Fig. 1, for m$_{N}$ ≲ M$_{W}$ where the DM particles dominantly annihilate into f ¯ f , the relic density further increases because of the small mixing angle. When the DM is heavier, the annihilation mode into Higgs boson pairs is opened and the relic density slightly deceases, but the reduction is not enough to reach Ω$_{N}$ h 2 ≃ 0 . 1.  0.001  0.01  0.1  1  10  100  1000  60  80  100  120  140  160  180  200 N h 2 m$_{N}$ [GeV] FIG. 1: The thermal relic density of RH neutrino DM as a function of its mass for a parameter set: ( v ′ , M$_{h}$, M$_{H}$, M$_{Z}$ ′ , sin θ ) = (3000 GeV , 120 GeV , 200 GeV , 1000 GeV , 0 . 7). Our model is quite analogous to the so-called gauge singlet scalar dark matter [16–18]. Some recent studies can be found in Refs. [19, 20]. In the gauge singlet scalar DM model, the thermal abundance is mainly controlled by the interactions between the SM Higgs boson and the DM particle. In our model, B − L Higgs VEV v ′ can play the same role for m$_{N}$ < M$_{W}$ , namely a larger v ′ corresponds to weaker coupling between DM and Higgs for a fixed DM mass. On the other hand, for m$_{N}$ > M$_{W}$ the difference appears. Even if the annihilation 6