Within the framework of the light-cone formalism we construct a model wave function appropriate for axial-vector mesons. The spin bilinear covariant component of our model wave function is consistent with the Melosh transformation procedure. We have applied our model to the {ital a}{sub 1} axial-vector meson and have compared the first six moments of the quark distribution amplitude with those obtained from the QCD sum-rule technique. In addition to our axial-vector-meson results, we further investigate the simple light-cone quark model by computing moments for pseudoscalar {pi} and {ital K} and vector {rho} mesons and compare our results with those from various QCD sum-rule techniques and lattice calculations.