In a travel safety system for a vehicle: a preceding vehicle V1 in a travel direction of a subject vehicle V is detected by a radar device; an overlap amount .delta. (smaller one of .delta.(L) and .delta.(R)), at which the preceding vehicle V1 overlaps a predicted course for the subject vehicle V, is calculated; and when time for which the over lap amount .delta. exceeding a predetermined value exceeds a predetermined period, it is determined that there is a possibility that the subject vehicle V comes into contact with the preceding vehicle V1, and a safety system comprising a warning or an automatic braking is actuated. Thus, if it is determined that there is a possibility of contact between the subject vehicle V and the preceding vehicle V1 due to course change of the subject vehicle V or the preceding vehicle, it is possible to prevent the safety system from being unnecessarily actuated to provide a sense of discomfort to a driver.