In normal driving conditions, drivers can usually anticipate with a good degree of accuracy the movements of vehicles ahead of them. Such anticipation can reduce the gaps between vehicles and produce high flows on freeway lanes. This anticipation effect is introduced in a car-following model in continuous space and discrete time, along with a set of driving rules that capture the car-following behavior of drivers. Detailed analysis shows that the model can simulate the full range of traffic conditions—free flow, congestion, and traffic jams under fixed and moving bottlenecks—and produce realistic flow capacities and fundamental diagrams with different levels of anticipation. Moreover, analysis of jam formation and decay reveals the underlying relationship between the parameters of the model and the triangular fundamental diagram. The platoon effect can be captured in the model by gap anticipation level (a) dependent on the gap.