  Motivated by recent results from the LHCb, BABAR and Belle collaborations on
B\to D^{(*)}\ell^-\bar{\nu}_\ell decays, which significantly deviate from the
Standard Model and hint the possible new physics beyond the Standard Model, we
probe the R-parity violating supersymmetric effects in B^-_c\to
\ell^-\bar{\nu}_\ell and B\to D^{(*)}\ell^-\bar{\nu}_\ell decays. We find that
(i) \mathcal{B}(B^-_c\to e^- \bar{\nu}_e) and
\mathcal{B}(B^-_c\to\mu^-\bar{\nu}_\mu) are sensitive to the constrained
slepton exchange couplings; (ii) the normalized forward-backward asymmetries of
B\to De^-\bar{\nu}_{e} decays have been greatly affected by the constrained
slepton exchange couplings, and their signs could be changed; (iii) all
relevant observables in the exclusive b\to c\tau^-\bar{\nu}_\tau decays and the
ratios \mathcal{R}(D^{(*)}) are sensitive to the slepton exchange coupling,
\mathcal{R}(D^*) could be enhanced by the constrained slepton exchange coupling
to reach each 95\% confidence level experimental range from BABAR, Belle and
LHCb, but it could not reach the lower limit of the 95\% confidence level
experimental average. Our results in this work could be used to probe R-parity
violating effects, and will correlate with searches for direct supersymmetric
signals at the running LHCb and the forthcoming Belle-II.
