The research on the car-following model of Connected and Autonomous Vehicles (CAVs) can provide a model reference for large-scale field testing in the future, and the model has become a research hotspot in the field of traffic flow and intelligent transportation. To better study the car-following characteristics of CAVs, this study proposes a car-following model BL-MVDAM considering the multiple preceding vehicle information and backward looking effect on the basis of the MVD model. The judgment basis for the traffic flow stability of the BL-MVDAM model is deduced by linear stability analysis. The effects of different parameters in the model on the system stability are analyzed. The analysis results are verified by a simulation experiment. In the experiment, a slight disturbance is applied to a vehicle group in the car-following process on a circular road. This experiment is designed according to the attention P of a car in the group to the follower and the number k of cars in front. The speed fluctuation of the vehicle group in the proposed model is small in comparison with the FVD, MVD, OMVC and BLVD models under the same initial conditions. Especially, when P is 0.8 and k is 3, the average speed fluctuation can be as low as 0.24%. The experimental results show that the model considering the multiple preceding vehicle information and backward looking effect has a better stability region, which can better absorb the disturbance and enhance the driving stability of a vehicle group.