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Abstract In this paper, we calculate the matrix element and form factors of vector-to- vector (V I → V II ) transition within the standard light-front (SLF) and covariant light- front (CLF) quark models (QMs), and investigate the self-consistency and Lorentz covari- ance of the CLF QM within two types of correspondences between the manifest covariant Bethe-Salpeter approach and the LF approach. The zero-mode and valence contributions to the form factors of V I → V II transition in the CLF QM and their relation to the SLF results are analyzed, and the main conclusions obtained via the decay constants of vector and axial-vector mesons and the form factors of P → V transition in the previous works are confirmed again. Furthermore, we present our numerical predictions for the form factors of c → (q, s) (q = u, d) induced D * → (K * , ρ), D ∗ → (ϕ, K * ), J/Ψ → D s ∗ D ∗ $$ \left({D}_s^{\ast },{D}^{\ast}\right) $$ , B c ∗ → B s ∗ B ∗ $$ {B}_c^{\ast}\to \left({B}_s^{\ast },{B}^{\ast}\right) $$ transitions and b → (c, s, q) induced B ∗ → (D ∗, K ∗, ρ), B s ∗ → D s ∗ ϕ K ∗ $$ {B}_s^{\ast}\to \left({D}_s^{\ast },\phi, {K}^{\ast}\right) $$ , B c ∗ → J / Ψ D s ∗ D ∗ , ϒ 1 S → B c ∗ B s ∗ B ∗ $$ {B}_c^{\ast}\to \left(J/\varPsi, {D}_s^{\ast },{D}^{\ast}\right),\varUpsilon (1S)\to \left({B}_c^{\ast },{B}_s^{\ast },{B}^{\ast}\right) $$ the relevant phenomenological studies of meson decays.