Due to the development of the modern scientific technology, autonomous vehicles may realize to connect with each other and share the information collected from each vehicle. An improved forward considering car-following model was proposed with mean expected velocity field to describe the autonomous vehicles flow behavior. The new model has three key parameters: adjustable sensitivity, strength factor and mean expected velocity field size. Two lemmas and one theorem were proven as criteria for judging the stability of homogeneousautonomous vehicles flow. Theoretical results show that the greater parameters means larger stability regions. A series of numerical simulations were carried out to check the stability and fundamental diagram of autonomous flow. From the numerical simulation results, the profiles, hysteresis loop and density waves of the autonomous vehicles flow were exhibited. The results show that with increased sensitivity, strength factor or field size the traffic jam was suppressed effectively which are well in accordance with the theoretical results. Moreover, the fundamental diagrams corresponding to three parameters respectively were obtained. It demonstrates that these parameters play almost the same role on traffic flux: i.e. before the critical density the bigger parameter is, the greater flux is and after the critical density, the opposite tendency is. In general, the three parameters have a great influence on the stability and jam state of the autonomous vehicles flow. •A new car-following model was proposed with mean expected velocity field.•Two lemmas and one theorem were proven as criteria for judging stability.•Stability and fundamental diagram were examined with different parameters.