By using the GRACE-Loop system, we calculate the full O(alpha) electroweak radiative corrections to the process e(+)e(-) -> 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 similar to-4% to similar to-21% when.7s 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. (C) 2014 The Authors. Published by Elsevier B.V.