To make full use of the newly available information provided by the intelligent transportation system (ITS), we presented a new car-following model applicable to automated driving control, which will be realized in the near future along with the rapid development of ITS. In this model, the backward-looking effect and the information inputs from multiple leading cars in traffic flow are considered at the same time. The linear stability criterion of this model is obtained using linear stability theory. Furthermore, the nonlinear analysis method is employed to derive the modified Korteweg-de Vries (mKdV) equation, whose kink-antikink soliton solution is then used to describe the occurrence of traffic jamming transitions. The numerical simulation of the presented model is carried out. Both the analytical analysis and numerical simulation show that the traffic jam is suppressed efficiently by just considering the information of two leading cars and a following one.