A measurement of the cross section for the inclusive production of isolated photons by the CDF experiment at the Fermilab Tevatron collider is presented. The measurement covers the pseudorapidity region |eta^gamma|<1.0 and the transverse energy range E_T^gamma>30 GeV and is based on 2.5/fb of integrated luminosity. The sample is almost a factor of seven larger than those used for recent published results and extends the E_T^gamma coverage by 100 GeV. The result agrees with next-to-leading order perturbative QCD calculations within uncertainties over the range 50<E_Tgamma<400 GeV, though the energy spectrum in the data shows a steeper slope at lower E_T^gamma.