Rail grinding as a part of maintenance of railway track is executed for the purpose of reducing damage on rails and environmental noise etc. When executing grinding to remove head checks at rail gauge corner in curve sections, the grinding-rail profile and grinding range should be carefully considered so as not to induce flange climb derailment. The authors have implemented numerical simulation of a vehicle running on ground rails in curve sections at a low speed, and examined running safety against flange climbing characterized by such factors as the wheel-load imbalance and curve radii. Based on the simulation results, a new indicator, which is concerned with the vertical displacement and the contact angle of a wheel on high rail, is proposed in order to evaluate the tolerable quantity to limits for securing safety against flange climb derailment. The indicator and the further consideration of the rail profile derive an acceptable condition of the grinding range of the rail profile and the curve radius in tracks.