Along with the rapid development of connected vehicle communication technology, describing the vehicle following driving status becomes gradually complicated. Driver behavior, vehicle type, and road factors affect vehicle speed, and the following distance reflects variability. In this paper, a nonlinear following distance model is constructed to characterize this variability. The model is based on the full speed difference model (FVD), and introduces the headway time distance coefficient, the following vehicle type coefficient, the communication advance response parameter reflecting the driver's personal characteristics, and the slope coefficient and curve curvature coefficient reflecting the road conditions, etc., and analyzes to obtain the stability conditions of the model. MATLAB is applied to numerical simulation experiments of the model, and the results show that the model can better describe the variability of following headway due to driver attributes, vehicle type, slope and curve in the connected vehicle scenario, thus providing a reference for traffic flow control and management.