Car taillights are ubiquitous during the deceleration process in real traffic,while drivers have a memory for historical information.The collective effect may greatly affect driving behavior and traffic flow performance.In this paper,we propose a continuum model with the driver's memory time and the preceding vehicle's taillight.To better reflect reality,the continuous driving process is also considered.To this end,we first develop a unique version of a car-following model.By converting micro variables into macro variables with a macro conversion method,the micro carfollowing model is transformed into a new continuum model.Based on a linear stability analysis,the stability conditions of the new continuum model are obtained.We proceed to deduce the modified KdV-Burgers equation of the model in a nonlinear stability analysis,where the solution can be used to describe the propagation and evolution characteristics of the density wave near the neutral stability curve.The results show that memory time has a negative impact on the stability of traffic flow,whereas the provision of the preceding vehicle's taillight contributes to mitigating traffic congestion and reducing energy consumption.