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In this article, we calculate the form-factors of the transitions $B \toa_1(1260)$, $b_1(1235) $ in the leading-order approximation using thelight-cone QCD sum rules. In calculations, we choose the chiral current tointerpolate the $B$-meson, which has outstanding advantage that the twist-3light-cone distribution amplitudes of the axial-vector mesons have nocontributions, and the resulting sum rules for the form-factors suffer frommuch less uncertainties. Then we study the semi-leptonic decays $B \toa_1(1260) l\bar{\nu}_l$, $b_1(1235) l\bar{\nu}_l$ $(l=e,\mu,\tau)$, and makepredictions for the differential decay widths and decay widths, which can beconfronted with the experimental data in the coming future.

$B \to A$ transitions in the light-cone QCD sum rules with the chiral current