Separating the mixture of the K1(1270) and K1(1400) states, the B → K1(1270, 1400)νν transition form factors are calculated in the three-point QCD sum rules approach. The longitudinal, transverse and total decay widths as well as the asymmetry parameter, characterizing the polarization of the axial K1(1270, 1400) and the branching ratio for these decays are evaluated. PACS numbers: 11.55.Hx, 13...