The spontaneous symmetry breaking (SSB) scheme is to realize the breaking pattern SU (2)$_{L}$ ⊗ SU (2)$_{R}$ ⊗ U (1)$_{B}$$_{−}$$_{L}$ → SU (2)$_{L}$ ⊗ U (1)$_{Y}$ → U (1)$_{em}$. After the SSB, the Higgs multiplets obtain nonzero VEVs where κ$_{1}$$_{,}$$_{2}$ , ξ$_{1}$$_{,}$$_{2}$ , v$_{L}$ and v$_{R}$ are in general complex, and κ ≡ $^{√}$| κ$_{1}$ | 2 + | κ$_{2}$ | 2 + | ξ$_{1}$ | 2 + | ξ$_{2}$ | 2 ≈ 246 GeV represents the electroweak symmetry breaking scale. The value of v$_{R}$ sets the scale of LR symmetry breaking which is directly linked to the right-handed gauge boson masses M$_{W}$$_{R}$ = gv$_{R}$$_{/}$√$_{2. It is required that}$ S$_{D}$ does not develop a VEV directly from V $_{0}$, namely CP is not broken by the singlet sector. It follows that after the SSB, although P and CP are both broken, there is a residual Z$_{2}$ type of discrete symmetry on S$_{D}$ in the gauge singlet sector, which is induced from the original CP symmetry. Constraints on the parameter space from the DM relic density has been discussed in Ref. [15]. The main DM annihilation channels are S$_{D}$S$_{D}$ → W $^{±}$W $^{∓}$, t ¯ t and SM-like Higgs boson h $^{0}$h$^{0}$. Making use of the constrained parameter space, we predicted the weakly interacting massive particle-nucleus elastic scattering cross section. The results show that the typical scattering cross section is about one order of magnitude below the current experimental upper bound. But in the enhanced Yukawa coupling case, the resulting spin-independent cross section can reach 10 − $^{44}$cm2 which is close to the improved bound set by the recent CDMS-II experiment [18]. The tiny soft C -breaking terms in V 1 may lead to the DM particle decay. The most general P -even but C -odd terms with dimension less than four are given by In this case, the S$_{D}$ may decay dominantly into two lighter scalars such as δ$_{L}$δ$_{L}$ . The lifetime of S$_{D}$ is estimated by 1 /τ$_{D}$ ≈ µ 2 ϵ $^{√}$1 − 4 m $^{2}$/m 2 $_{D}$/ (16 πm$_{D}$ ) for m ≪ m$_{D}$ , where m$_{D}$ and m stand for the mass of S$_{D}$ and final state scalars respectively. In order to have a lifetime around O (10 $^{26}$s), the required value of µ$_{ϵ}$ is around 10 − 23 GeV. In this work we focus on the case in which ζ$_{1}$ ≫ ζ$_{i}$ ( i = 2 , . . . , 7) and the right-handed triplet Δ$_{R}$ is much heavier than that of S$_{D}$ , such that S$_{D}$ will decay dominantly into left- handed triplet Δ$_{L}$ as shown in Fig. 1. 6 −V 1 = µ$_{ϵ}$ ( S − S $^{∗}$)$^{[}$ 5 ∑ i =1 ζ$_{i}$O$_{i}$ + ζ$_{6}$ ( S + S $^{∗}$) 2 + ζ$_{7}$ ( S − S $^{∗}$) 2 ] . (9) 〈 δ 0 L,R 〉 = v$_{L,R}$ √$_{2}$ , 〈 φ 0 1 , 2 〉 = κ$_{1}$$_{,}$$_{2}$ √$_{2}$ and 〈 χ 0 1 , 2 〉 = ξ$_{1}$$_{,}$$_{2}$ √$_{2}$ , (8)