  In a few years, the COMET experiment at J-PARC and the Mu2e experiment at
Fermilab will probe the $\mu-e$ conversion rate in the vicinity of
$\mathcal{O}(10^{-17})$ for an Al target with high experimental sensitivity.
Within the framework of the minimal supersymmetric extension of the Standard
Model with local $B-L$ gauge symmetry (B-LSSM), we analyze the lepton flavor
violating (LFV) process of $\mu-e$ conversion in nuclei. Considering the
constraint of the experimental upper limit of the LFV rare decay
$\mu\rightarrow e\gamma$, the $\mu-e$ conversion rates in nuclei within the
B-LSSM can achieve $\mathcal{O}(10^{-12})$, which is 5 orders of magnitude
larger than the future experimental sensitivity at the Mu2e and COMET
experiments and may be detected in the near future.
