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 make 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)l■l,b 1(1235)l■l(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.