In this paper, we report the production cross-section of forward photons in the pseudorapidity regions of $eta,>,10.94$ and $8.99,>,eta,>,8.81$, measured by the LHCf experiment with proton--proton collisions at $sqrt{s}$ = 13 TeV. The results from the analysis of 0.191 $mathrm{nb^{-1}}$ of data obtained in June 2015 are compared to the predictions of several hadronic interaction models that are used in air-shower simulations for ultra-high-energy cosmic rays. Although none of the models agree perfectly with the data, EPOS-LHC shows the best agreement with the experimental data among the models.