We analyze the semileptonic rare decays of the B meson to K-1(1270) and K-1(1400) axial vector mesons. The B -> K-1(1270, 1400)l(+)l(-) decays are significant flavor-changing neutral current decays of the B meson. These decays are sensitive to the new physics beyond the standard model (SM), since these processes are forbidden at tree level at SM. These decays occurring at the quark level via b -> sl(+)l(-) transition also provide new opportunities for calculating the CKM matrix elements V-bt and V-ts. In this study, the transition form factors of the B -> K-1(1270, 1400)l(+)l(-) decays are calculated using the three-point QCD sum rules approach. The resulting form factors are used to estimate the branching fractions of these decays.