  We investigate the ${\mathcal{R}}(D)$ and ${\mathcal{R}}(D^{\ast})$ anomalies
in the context of the $B-L$ extension of the Minimal Supersymmetric Standard
Model with Inverse Seesaw. We demonstrate that the lepton penguin $W^{\pm}l
\bar\nu_l $ ($l=e,\mu,\tau$) mediated by CP-even/odd right-handed sneutrinos,
charginos and neutralinos can account for these anomalies simultaneously.
