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We present the production cross-section of gamma-rays based on data of p-pcollisions at LHC, revising the previous semi-empirical formula mainly for 1)the inelastic cross-section in p-p collisions, $\sigma_{pp}(E_0)$, and 2) theinclusive gamma-ray spectrum in the forward region, $\sigma_{pp \rightarrow\gamma}(E_0, E_\gamma)$. We find that the previous cross-section gives asignificantly softer spectrum than found in the data of LHC. In this paper, wefocus our interest mainly upon the LHC forward (LHCf) experiment, givinggamma-ray spectra in the very forward region with the pseudo-rapidity $\eta^*$> 8.8 in the center of mass system (CMS), which have not been reported so far.We also give the pseudo-rapidity distribution of charged hadrons with -3 <$\eta^*$ < 3 obtained by ALICE and TOTEM experiments, both with LHC. We findthat the revised cross-section reproduces quite well the accelerator data overthe wide energy range from GeV to 30 PeV for projectile protons, correspondingapproximately to 100 MeV to 3 PeV for secondary gamma-rays. The productioncross-section of gamma-rays produced in the forward region is essential for thestudy of gamma-ray astronomy, while not important are those produced in thecentral region in CMS, and of much less importance in the backward. We discussalso the average transverse momentum of gamma-rays, $\bar{p}_{t}$, and theaverage inelasticity transferred to gamma-rays, $\bar{k}_\gamma^*$, obtainingthat the former increases very slowly with $\bar{p}_{t}$ = 100 - 220 MeV/c for$E_0$ = 1 GeV - 26 PeV, and the latter is almost independent of $E_0$, with$\bar{k}_\gamma^* \approx 1/6$, while we can not exclude the possibility of asmall increase of $\bar{k}_\gamma^*$.

Revised production cross-section of gamma-rays in p-p collisions with LHC data for the study of TeV gamma-ray astronomy