Recently, the research on traffic flow system based on some classical models, such as cellular automata and car-following models, has attracted much attention. Some meaningful achievements have been obtained in the past few years by scholars from various fields. This paper starts with literature review on traffic flow theory studies. Car-following models, including the initial model proposed by Newell in 1961 (Newell G F 1961 Oper. Res. 9 209) and some later modified ones (e.g. full velocity difference model, or FVD model for short) have been deeply investigated. Based on Newell's car-following model, an extension of car-following model with consideration of vehicle-to-vehicle (V2V) communication is then developed. The vehicle-to-vehicle communication technology, which was proposed in the early 2000s, enable vehicles to collect traffic condition information from other vehicles (e.g. speed, headway, position, acceleration, etc.) and provide them for drivers in almost real time. Compared with those without V2V devices, drivers with information from V2V devices can react to traffic flow fluctuation timelier and more precisely. To represent the pre-reaction of drivers to traffic flow information provided by V2V devices, a parameter, , is newly introduced into Newell's car-following model. Then by second-order Taylor series expansion, a new car-following model with the influence of V2V (called V2V model) is proposed. Neutral stability condition of V2V model as well as phase diagram is derived theoretically with linear analysis method. The phase diagram of linear stability condition is divided into stable and unstable regions. By analyzing stability performance of the proposed model, it is evident that V2V communication technology can improve the stability of traffic flow system. Numerical simulation is demonstrated to study the influence of V2V devices on traffic flow on the one hand, and to acquire density waves as well as hysteresis loops under different values of parameter on the other hand. The sensitive analysis method are adopted as well.The numerical simulation results indicate that: 1) when compared with FVD model, V2V model can make vehicles react to traffic flow fluctuation earlier and reduce the speed changes under start-up, brake and incident conditions; this indicates that the consideration of V2V devices can improve the safety and ride comfort of traffic flow system; 2) the V2V model is sensitive to the value changes of parameter and T; the stability of traffic flow can be improved if the value of parameter increases, or parameter T decreases; this outcome precisely agrees with the above theoretical analysis; 3) the characteristics of traffic flow can influence the performance of V2V technology: compared with under low density condition, V2V communication technology can significantly increase the average speed of traffic flow under high density condition.