A measurement of the cross section for the inclusive production of isolated prompt photons in proton-proton collisions at a centre-of-mass energy of s√=8 TeV is presented. The measurement covers the pseudorapidity ranges |ηγ | < 1.37 and 1.56 ≤ |ηγ | < 2.37 in the transverse energy range 25 < EγT < 1500 GeV. The results are based on an integrated luminosity of 20.2 fb−1, recorded by the ATLAS detector at the LHC. Photon candidates are identified by combining information from the calorimeters and the inner tracker. The background is subtracted using a data-driven technique, based on the observed calorimeter shower-shape variables and the deposition of hadronic energy in a narrow cone around the photon candidate. The measured cross sections are compared with leading-order and next-to-leading order perturbative QCD calculations and are found to be in a good agreement over ten orders of magnitude.