In this work we have studied hadronic charmless two-body B decays involving p-wave mesons in final state.We have calculated branching ratios of B → AT decays (where A and T denotes a 3 P1 axial-vector and a tensor meson, respectively), using B → T form factors obtained in the covariant light-front (CLF) approach, and the full effective Hamiltonian.We have obtained that2 ) = (5.91 -6.42) × 10 -6 with θ3 P 1 = 27.9 1270), K1(1400).It seems that these decays can be measured in experiments at B factories.Additionally, we have found that B(B → K1(1270)a2)/B(B → K1(1400)a2) and B(B → f1(1420)K *2 )/B(B → f1(1285)K * 2 ) ratios could be useful to determine numerical values of mixing angles θK 1 and θ3 P 1 , respectively.