Starting from the full velocity difference model, an extended car-following model is proposed by considering the influence that in real traffic the driver’s forecast has an effect on car-following behavior of traffic flow. The mechanism how the stability and energy dissipation of traffic flow are in fluenced by the driver’s forecast effect is revealed by the application of the proposed new model. The linear stability condition of the new model is derived theoretically through linear stability theory. The phase diagram of linear stability condition is divided into two regions by each stability curve: the stable and unstable regions. And the corresponding stable region will be enlarged with the increase of driver’s forecast time, hence the traffic condition will be improved through considering driver’s forecast effect. By numerical simulation method, the space-time evolution relation between the velocity and headway of vehicles in car-following queue is investigated systematically under the influence of driver’s forecast. In the same time, the evolution mechanisms of the overall average energy dissipation of traffic flow and individual vehicle energy consumption with the addition of small disturbance are discussed explicitly under a periodic condition, and it is discovered that the overall average energy consumption in traffic flow and the energy dissipation of individual vehicle is accompanied by a complex critical phase transition process. Good agreement between the numerical simulation and the theoretical analysis show that by considering of driver’s forecast effect, not only the stability of traffic flow is enhanced obviously, but the energy consumption is reduced remarkably as we expect. Furthermore, it is verified that both the overall average energy consumption of the considered traffic flow and the energy consumption of an individual vehicle are reduced gradually along with the increase of driver’s forecast time. On the other hand, numerical simulation results verify that the shortcoming of negative speed appearing in the full velocity difference model with low reaction coefficient can be effectively avoided by increasing the driver’s forecast time in the improved model, which means that the dynamic characteristics of traffic flow can be described more precisely by the proposed model.