Runway excursions are the main risk for runway safety: operational protection areas mitigate the effects of events classified as veer-off, overrun, and undershoot. This paper presents a methodology for the quantitative risk assessment of runway veer-off in an international airport whose name will not be revealed for privacy reasons. The proposed methodology is based on similar principles adopted in other aviation risk analyses. The Real Level of Safety (RLS) related to the veer-off accident was calculated through the implementation of a retrospective analysis that permits to define a frequency model, a location model and a consequence model. Instead, Target Level of Safety (TLS) was defined through the risk matrix and acceptability criteria present in the International Civil Aviation Organization (ICAO) Safety Management Manual. Finally, the risk of veer-off accidents in the airport under evaluation was determined by using primary data provided by the airport management body. Risk values were calculated in more than 1300 points around the runway and they were used to assess the current level of safety. The authors present a risk map that allows identifying the areas in the strip with the highest risk of a veer-off accident. The obtained results demonstrate that the developed methodology represents a useful tool to define TLS and to assess whether infrastructural and operational modification need to obtain the required level of safety.