  There are strong evidences for existence of dark matter in some experiments
at present. However, the question is that we do not have a reasonable
explanation for dark matter in the framework of the Standard Model(SM) of
particle physics. It is necessary to extend the SM in order to explain the dark
matter. According to the current possible existence conditions of dark matter,
we choose $\chi^0_L$ and $\tilde{Y}$ as candidates for dark matter in the
EBLMSSM. We study the dominant annihilation processes in detail, including
$\bar{\chi}^0_L\chi^0_L(\bar{\tilde{Y}}\tilde{Y})\rightarrow \bar{l}^Il^I$ and
$\bar{\chi}^0_L\chi^0_L(\bar{\tilde{Y}}\tilde{Y})\rightarrow \bar{\nu}^I\nu^I$.
And we calculate their annihilation cross section $\sigma$ and relic density
$\Omega_D h^2$. Then we analyze the limitations of dark matter relic density on
the parameters of the EBLMSSM.
