  This study investigates the excesses observed in the diphoton and $b\bar b$
data around $95\;{\rm GeV}$ within the framework of the $B-L$ supersymmetric
model (B-LSSM). Comparing with the minimal supersymmetric standard model, the
B-LSSM incorporates two singlet chiral Higgs bosons which mix with the SM-like
Higgs boson due to the gauge kinetic mixing effect. The richer Higgs sector
indicates that designating the B-LSSM specific CP-even Higgs state as the
lightest Higgs boson has great potential to explain the excesses at around
$95\;{\rm GeV}$. Considering the two-loop effective potential corrections to
the squared Higgs mass matrix, it is found that the signal strengthes
$\mu(h_{95})_{\gamma\gamma}$, $\mu(h_{95})_{b b}$ can be described
simultaneously in the experimental $1\sigma$ interval. And the B-LSSM specific
parameters $\tan\beta'$, $B_\eta$, $g_{YB}$, $M_{Z'}$ affect the theoretical
predictions on the light Higgs boson masses and signal strengthes
$\mu(h_{95})_{\gamma\gamma}$, $\mu(h_{95})_{bb}$ significantly.
