We present the production cross-section of γ-rays based on data of p-p collisions at the Large Hadron Collider (LHC), revising the previous semi-empirical formula mainly for 1) the inelastic cross-section in p-p collisions, σ pp (E 0 ), and 2) the inclusive γ-ray spectrum in the forward region, σ pp→γ (E 0 , E γ ). We find that the previous cross-section gives a significantly softer spectrum than found in the data of LHC. In this paper, we focus our interest mainly upon the LHC forward (LHCf) experiment, giving γ-ray spectra in the very forward region with the pseudo-rapidity η * > ∼ 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 ≤ η * ≤ 3 obtained by ALICE and TOTEM experiments, both with LHC. We find that the revised cross-section reproduces quite well the accelerator data over the wide energy range from GeV to 30 PeV for projectile protons, corresponding approximately to 100 MeV to 3 PeV for secondary γ-rays. The production cross-section of γ-rays produced in the forward region is essential for the study of γ-ray astronomy, while not important are those produced in the central region in CMS, and of much less importance in the backward. We discuss also the average transverse momentum of γ-rays,p t , and the average inelasticity transferred to γ-rays,k * γ , obtaining that the former increases very slowly withp t = 100 ∼ 220 MeV/c for E 0 = 1 GeV ∼ 26 PeV, and the latter is almost independent of E 0 , withk * γ ≈ 1/6, while we can not exclude the possibility of a small increase ofk * γ .