We propose a new detection method to predict a vehicle’s trajectory and use it for detecting lane changes of surrounding vehicles. According to the previous research, more than 90% of the car crashes are caused by human errors, and lane changes are the main factor. Therefore, if a lane change can be detected before a vehicle crosses the centerline, accident rates will decrease. Previously reported detection methods have the problem of frequent false alarms caused by zigzag driving that can result in user distrust in driving safety support systems. Most cases of zigzag driving are caused by the abortion of a lane change due to the presence of adjacent vehicles on the next lane. Our approach reduces false alarms by considering the possibility of a crash with adjacent vehicles by applying trajectory prediction when the target vehicle attempts to change a lane, and it reflects the result of lane-change detection. We used a traffic dataset with more than 500 lane changes and confirmed that the proposed method can considerably improve the detection performance.