The cross-section for the $\pi^{+} \pi^{-} \pi^{0}$ invariant mass distribution in the $\gamma p$ reaction in the GeV region is calculated. This reaction is assumed to proceed through the formation of the 𝜔-meson in the intermediate state, because the production cross-section for this meson in the $\gamm p$ reaction in the GeV region is significant and it has a large branching ratio (88.8%) in the $\pi^{+} \pi^{−} \pi^{0}$ channel. The cross-sections for this reaction are calculated using the energy-dependent reaction amplitude, $f_{\gamma p \rightarrow \omega p (0)$, extracted from the latest 𝜔-meson photoproduction data. We use established procedure to calculate other factors, like width and propagator of the 𝜔-meson, so that our calculation can provide reliable cross-section. The calculated results reproduce the measured $\pi^{+} \pi^{-} \pi^{0}$ invariant mass distribution spectra in the $\gamma p$ reaction.