By using the GRACE-Loop system, we calculate the full O(alpha) electroweak radiative corrections to the process e+e- gamma, which is important for future investigations at the International Linear Collider (ILC). With the GRACE-Loop system, the calculations are checked numerically by three consistency tests: ultraviolet finiteness, infrared finiteness, and gauge-parameter independence. The results show good numerical stability when quadruple precision is used. In the phenomenological results, we find that the electroweak corrections to the total cross section range from ~-4% to ~-21% when s varies from 250 GeV to 1 TeV. The corrections also significantly affect the differential cross sections, which are a function of energies and angles of the final state particles. Such corrections will play an important role in the high-precision program at the ILC.