  The difference between the updated experimental result on the muon anomalous
magnetic dipole moment and the corresponding theoretical prediction of the
standard model on that is about $4.2$ standard deviations. In this work, we
calculate the muon anomalous MDM at the two-loop level in the supersymmetric
$B-L$ extension of the standard model. Considering the experimental constraints
on the lightest Higgs boson mass, Higgs boson decay modes $h\rightarrow
\gamma\gamma,\;WW,\;ZZ,\; b\bar b,\;\tau\bar\tau$, B rare decay $\bar
B\rightarrow X_s\gamma$, and the transition magnetic moments of Majorana
neutrinos, we analyze the theoretical predictions of the muon anomalous
magnetic dipole moment in the $B-L$ supersymmetric model. The numerical
analyses indicate that the tension between the experimental measurement and the
standard model prediction is remedied in the $B-L$ supersymmetric model.
