Direct photon production at mid-rapidity in Pb–Pb collisions at ainer hidden"> was studied in the transverse momentum range 0.9<pT<14 GeV/cainer hidden">. Photons were detected with the highly segmented electromagnetic calorimeter PHOS and via conversions in the ALICE detector material with the e+e−ainer hidden"> pair reconstructed in the central tracking system. The results of the two methods were combined and direct photon spectra were measured for the 0–20%, 20–40%, and 40–80% centrality classes. For all three classes, agreement was found with perturbative QCD calculations for pT≳5 GeV/cainer hidden">. Direct photon spectra down to pT≈1 GeV/cainer hidden"> could be extracted for the 20–40% and 0–20% centrality classes. The significance of the direct photon signal for 0.9<pT<2.1 GeV/cainer hidden"> is 2.6σ for the 0–20% class. The spectrum in this pTainer hidden"> range and centrality class can be described by an exponential with an inverse slope parameter of (297±12stat±41syst) MeVainer hidden">. State-of-the-art models for photon production in heavy-ion collisions agree with the data within uncertainties.