Photon-pair direct or jet-associated production is important for relevant standard model measurement, Higgs and new physics searches at the Large Hadron Collider (LHC). The loop-induced gluon-fusion process gg -> gamma gamma g, which formally contributes only at the next-to-next-to-leading order to gamma gamma j productions, may get enhanced by the large gluon flux at the LHC. We have checked and confirmed previous results on gg -> gamma gamma (Dicus and Willenbrock 1988 Phys. Rev. D37 1801), gamma gamma g (de Florian andKunszt 1999 Phys. Lett. B 460 184) at one loop, using the traditional Feynman diagram based approach, taking into account the quark mass effects, and updated them further for the 7 and 14 TeV LHC with new inputs and settings. We provide the details and results of the calculations, which involve manipulation of rank-5 pentagon integrals. Our results show that the gluon-fusion process can contribute about 10% of the Born result, especially at small M-gamma gamma and P-gamma gamma(T), and increase further the overall scale uncertainty. Top quark loop effects are examined in detail, which become important near or above the threshold M-gamma gamma greater than or similar to 2m(t).