A precision measurement for the production of a -boson in association with two photons is important for investigating the Higgs boson and exploring new physics at the International Linear Collider. It could be used to study the anomalous quartic gauge coupling. In this work we report on our calculation of the full contributions to the process in the standard model, and we analyze the electroweak (EW) quantum effect on the total cross section. We investigate the dependence of the production rate on the event selection scheme and provide distributions for some important kinematic observables. We find that the next-to-leading order (NLO) EW corrections can enhance the total cross section quantitatively from 2.32 to when the colliding energy goes up from GeV to TeV, and the NLO EW corrections show obviously a nontrivial phase space dependence. We conclude that in studying the signal process , the background process can be suppressed significantly if we take appropriate kinematic cuts on the final products.