This article presents a search for flavour-changing neutral currents in the decay of a top quark into an up-type (q = c, u) quark and a Higgs boson, where the Higgs boson decays into two photons. The proton-proton collision data set analysed amounts to 36.1 fb−1 at √s=13 TeV collected by the ATLAS experiment at the LHC. Top quark pair events are searched for, where one top quark decays into qH and the other decays into bW . Both the hadronic and leptonic decay modes of the W boson are used. No significant excess is observed and an upper limit is set on the t → cH branching ratio of 2.2 × 10−3 at the 95% confidence level, while the expected limit in the absence of signal is 1.6 × 10−3. The corresponding limit on the tcH coupling is 0.090 at the 95% confidence level. The observed upper limit on the t → uH branching ratio is 2.4 × 10−3.