In studies of the dense medium produced in ultra-relativistic heavy ion collisions, photons are important hard probes, since they are not expected to be modified by the medium. The measurement of isolated prompt photon production in Pb–Pb collisions provides a test of perturbative quantum chromodynamics and the information to constrain the nuclear parton distribution functions. CMS has shown photon purity measurement capabilities in pp collisions using the shower shape templates. In Pb–Pb collisions at CMS, this technique was applied for the first time in heavy ion collisions. We report the first measurement of the transverse momentum spectra of isolated photons with pT from 20 to 80 GeV/c in Pb–Pb collisions at = 2.76 TeV. The centrality dependence of the nuclear modification factor is also reported by comparing the result to the photon spectrum of pp reference which is computed from NLO calculations.