In this article, we calculate the form-factors of the transitions B → a1（1260）, b1（1235） in the leading-order approximation using the light-cone QCD sum rules. In calculations, we choose the chiral current to interpolate the B-meson, which has the outstanding advantage that the twist-3 light-cone distribution amplitudes of the axial-vector mesons makes no contributions, and the resulting sum rules for the form-factors suffer from far fewer uncertainties. Then we study the semi-leptonic decays B → a1（1260） lvl, b1（1235） lvl （l=e,μ,τ）, and make predictions for the differential decay widths and decay widths, which can be compared with the experimental data in the coming future
