We reanalyze the B → M tensor form factors in a covariant light-front quark model, where M represents a vector meson V , an axial-vector meson A, or a tensor meson T . The treatment of masses and mixing angles in the K 1A,1B systems is improved, where K 1A and K 1B are the 3 P 1 and 1 P 1 states of the axial-vector meson K 1 , respectively. Rates of B → M γ decays are then calculated using the QCD factorization approach.