  The recent intriguing measurements of $R_{K}$ and $R_{K^*}$ are important
hints of new physics that violates lepton universality. We analyze the
semileptonic decays $b \to s \ell^+ \ell^-$ in the framework of the $B-L$
extension of Minimal Supersymmetric Standard Model (MSSM) with Inverse Seesaw
(BLSSMIS). A salient feature of this model is that one of the right-handed
sneutrino can be light and the neutrino Yukawa couplings are of order one. We
show that the box diagram mediated by right-handed sneutrino, higgsino-like
chargino, and light stop can account simultaneously for both $R_{K}$ and
$R_{K^*}$. Therefore, while the MSSM cannot explain the $R_K$ and $R_{K^*}$
anomalies, the BLSSMIS can account for them, where a significant lepton flavor
non-universality might stem from large neutrino Yukawa couplings.
