  In this paper we study the lepton polarization asymmetry for the simileptonic
OZI-forbidden annihilation B^-_c->\eta' \ell^- \bar{\nu} decay where \ell=\mu,
\tau. Our results show that the branching ratio turn out to be of order
10^{-4}. Beside, we find that longitudinal, transversal and normal components
of lepton polarizations can be measured for both \mu and \tau decay modes in
the future experiments at the LHC.
