We investigate the radiative decay of pseudoscalar (π, K, η, η ), vector (ρ, K * , ω, φ) and axial-vector (A 1 ) mesons using a simple relativistic constituent quark model. For both simplicity and relativity, we take advantage of the distinguished features in the light-cone quantization method: (1) the Fock state expansion of meson wave functions are not contaminated by the vacuum fluctuation, (2) the problem of assigning quantum numbers J P C to mesons is circumvented by the Melosh transformation. Except the well-known constituent quark masses of (u, d, s) quarks and the spin-averaged meson masses, the only parameter in the model is the Gaussian parameter β which determines the broadness (or sharpness) of the radial wave function. Our overall predictions of pseudoscalar, vector and axial-vector meson radiative decay processes are in remarkably good agreement with the experimental data.