Car-following theory is of significance in microscopic traffic flow theory. The key assumption of current car-following theory is that vehicles travel in the middle of a single lane. However, this assumption is unrealistic and cannot describe driving behavior in a complex traffic environment. When the lateral separation characteristics between the follower and the leader are taken into account, the time-to-collision equation is modified with visual angle information and introduced into the General Motors model. A non-lane-based model of car following was developed; it uses time to collision and is based on the stimulus–response framework. The proposed model was investigated with simulations conducted under several driving scenarios. The model could describe local and asymptotic stabilities, lateral movement, and the effect of neighboring vehicles. Results implied that this staggered car-following model incorporating lateral separation greatly enhanced the realism of car-following behavior.