  The MSSM is extended to the $U(1)_X$SSM, whose local gauge group is $SU(3)_C
\times SU(2)_L \times U(1)_Y \times U(1)_X$. To obtain the $U(1)_X$SSM, we add
the new superfields to the MSSM, namely: three Higgs singlets
$\hat{\eta},~\hat{\bar{\eta}},~\hat{S}$ and right-handed neutrinos
$\hat{\nu}_i$. It can give light neutrino tiny mass at the tree level through
the seesaw mechanism. The study of the contribution of the two-loop diagrams to
the MDM of muon under $U(1)_X$SSM provides the possibility for us to search for
new physics. In the analytical calculation of the loop diagrams (one-loop and
two-loop diagrams), the effective Lagrangian method is used to derive muon MDM.
Here, the considered two-loop diagrams include Barr-Zee type diagrams and
rainbow type two-loop diagrams, especially Z-Z rainbow two-loop diagram is
taken into account. The obtained numerical results can reach
$7.4\times10^{-10}$, which can remedy the deviation between SM prediction and
experimental data to some extent.
