Aiming at the limitations of single-dimensional car-following model to describe vehicle car-following behavior in local multi-vehicle environment, the mechanism of vehicles in adjacent lane influencing the subject vehicle car-following behavior is explored, and a vehicle car-following model more suitable for local multi-vehicle environment is attempted to be established. The driving behavior variable reflecting the influence of vehicles in adjacent lane was determined by correlation analysis. Vortisch indicator of similarity(VIS) was used to characterize the influence of vehicles in adjacent lane on car-following behavior. Chi-square independent test and kernel density curve were used to determine the VIS demarcation threshold reflecting whether the influence is significant. Recursive feature elimination was used to screen the variables related to car-following samples significantly affected by vehicles in adjacent lane. The influence mechanism of variables was determined according to the statistical analysis results. Based on the mechanism proposed, the car-following model suitable for local multi-vehicle environment was constructed and its prediction effect was evaluated. Results show that VIS between the speed of subject vehicle and following vehicle in adjacent lane can characterize the influence and the VIS threshold is 0.668. It is concluded that the attention mechanism and memory effect can explain the influence mechanism of car-following behavior in multi-vehicle environment. Considering the attention mechanism and memory effect, RMSE decrease by 65%in Full Velocity Difference Model (FVD) model and 62%in Intelligent Driver Model (IDM) model, MAE decrease by 65%and 59%and R2 increased by 180%and 288%respectively, which proved the rationality of the attention mechanism and memory effect in explaining the car following behavior of subject vehicle in local multi-vehicle environment.