  In order to meet the requirement of BBN, the right handed neutrino is added
to the singlet Higgs sector in the GNMSSM. The spectrum and Feynman rules are
calculated. the dark matter phenomenology is also studied. In case of $\l\sim
0$, the singlet sector can give perfect explanation of relic abundance of dark
matter and small cosmological structure simulations. The BBN constraints on the
light mediator can be easily solved by decaying to the right handed neutrino.
When the $\l_N$ is at the order of $\mathcal{O}(0.1)$, the mass of the mediator
can be constrained to several MeV
