Measurements of Higgs boson production cross sections with the Higgs boson decaying into a pair of photons are reported. Events with two photons are selected from a sample of proton-proton collisions at a centre-of-mass energy of 13 TeV collected by the Compact Muon Solenoid detector at the Large Hadron Collider in 2016 and 2017, corresponding to a total integrated luminosity of 77.4/fb. Cross sections for gluon fusion and vector boson fusion production, relative to the corresponding standard model predictions, are measured to be 1.15 ± 0.15 and 0.83 +0.37 −0.31 respectively. These two production modes are further measured in kinematic regions within the simplified template cross section framework. All results are found to be in agreement with the standard model expectations.