In order to better simulate the car-following characteristics, based on the full velocity difference (FVD) model, an improved FVD car-following model based on dynamic safety distance was proposed, which considers the headway, velocity difference, velocity and acceleration between the front and rear cars. A variable time headway model was constructed to quantify the influence of front vehicle acceleration on car-following distance. The linear stability analysis of the model was carried out by applying small amplitude perturbation analysis and long-wave expansion, and the critical stability conditions of the improved FVD model were derived. The numerical simulation experiment of micro-disturbance on the annular road was designed. The characteristics of vehicle following behavior after disturbance were analyzed, and the influence of acceleration parameters on the anti-disturbance ability of the model was analyzed. The results show that considering the acceleration information of the front vehicle can reduce the fluctuation amplitude during the disturbance evolution, which is helpful to improve the stability of the traffic flow.