  In the framework of the MSSM extension with local gauged baryon and lepton
numbers (BLMSSM), we calculate the muon anomalous magnetic dipole moment (MDM)
and lepton $(e, \mu, \tau)$ electric dipole moment (EDM), and discuss how the
muon MDM and lepton EDM depend on the parameters within the mass insertion
approximation. Among many parameters, $\tan{\beta}$,~$g_L$,~$m_L$ and $\mu_H$
are more sensitive parameters for $a^{BL}_{\mu}$. Considering the experimental
limitations, our best numerical result of $a^{BL}_{\mu}$ is around $2.5 \times
10^{-9}$, which can well compensate the departure between the experiment data
and Standard Model (SM) prediction. The CP violating phases in BLMSSM are more
than those in the MSSM, including new parameters $\theta_{\mu_L}$ and
$\theta_{L}$. They can give large contributions, which play an important role
in exploring the source of CP violation and probing new physics beyond SM.
