  We present a phenomenological model for the $\gamma\gamma \to
\pi^+\pi^-\pi^0$ reaction by including the production mechanism of the
$a_2(1320)$ resonance, as well as the contributions from the $\sigma/f_0(500)\,
\pi^0$ and $f_2(1270)\, \pi^0 $ production channels. Furthermore, the
$\gamma\gamma\to\rho^{\pm} \pi^{\mp}\to\pi^{+}\pi^-\pi^0$ channel, which is
essential for a description in the low-energy region, is investigated carefully
by introducing the complete set of gauge invariant and Lorentz-covariant
tensors for the $\gamma\gamma\to\rho^\pm \pi^\mp$ subprocess. The full
amplitude is constructed to yield a correct high-energy Regge behavior. Within
our model, we achieve a very reasonable description of ARGUS and L3 data of the
total cross section, as well as of the $\pi^\pm\pi^0$ and $\pi^+\pi^-$
invariant mass distributions. We also predict the invariant mass distributions
in the $\gamma\gamma$ center-of-mass energy range from $0.8$ GeV to $2.0$ GeV,
which will be studied by the forthcoming data of the BESIII collaboration.
