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The meson-photon transition form factors $\gamma\gamma^*\to P$ ($P$ standsfor $\pi$, $\eta$ and $\eta'$) provide strong constraints on the distributionamplitudes of the pseudoscalar mesons. In this paper, these transition formfactors are calculated under the light-cone perturbative QCD approach, in whichboth the valence and non-valence quarks' contributions have been taken intoconsideration. To be consistent, an unified wavefunction model is adopted toanalyze these form factors. It is shown that with proper charm component$f^{c}_{\eta'}\sim -30$ MeV and a moderate DA with $B\sim 0.30$, theexperimental 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 detaileddiscussion on the form factors' uncertainties caused by the constituent quarkmasses $m_q$ and $m_s$, the parameter $B$, the mixing angle $\phi$ and$f_{\eta'}^c$ are presented. It is found that by adjusting these parameterswithin their reasonable regions, one can improve the form factor to a certaindegree but can not solve the puzzle for $Q^{2}F_{\pi\gamma}(Q^2)$, especiallyto explain the behavior of $\pi-\gamma$ form factor within the whole $Q^2$region consistently. We hope further experimental data on these form factors inthe large $Q^2$ region can clarify the present situation.

Constraints on the Light Pseudoscalar Meson Distribution Amplitudes from Their Meson-Photon Transition Form Factors