  The meson-photon transition form factors $\gamma\gamma^*\to P$ ($P$ stands
for $\pi$, $\eta$ and $\eta'$) provide strong constraints on the distribution
amplitudes of the pseudoscalar mesons. In this paper, these transition form
factors are calculated under the light-cone perturbative QCD approach, in which
both the valence and non-valence quarks' contributions have been taken into
consideration. To be consistent, an unified wavefunction model is adopted to
analyze these form factors. It is shown that with proper charm component
$f^{c}_{\eta'}\sim -30$ MeV and a moderate DA with $B\sim 0.30$, the
experimental data on $Q^{2}F_{\eta\gamma}(Q^2)$ and $Q^{2}F_{\eta'\gamma}(Q^2)$
in whole $Q^2$ region can be explained simultaneously. Further more, a detailed
discussion on the form factors' uncertainties caused by the constituent quark
masses $m_q$ and $m_s$, the parameter $B$, the mixing angle $\phi$ and
$f_{\eta'}^c$ are presented. It is found that by adjusting these parameters
within their reasonable regions, one can improve the form factor to a certain
degree but can not solve the puzzle for $Q^{2}F_{\pi\gamma}(Q^2)$, especially
to explain the behavior of $\pi-\gamma$ form factor within the whole $Q^2$
region consistently. We hope further experimental data on these form factors in
the large $Q^2$ region can clarify the present situation.
