Unsafe lane-changing behaviors can easily lead to traffic accidents. Drivers usually turn on their turn signals to signal surrounding vehicles before changing lanes. At present, there is a lack of consideration of the impact of turn signals on the lane-changing behavior of intelligent vehicles. Therefore, based on the cellular automata theory, this paper improves the lane-changing rules in the STNS model and proposes a vehicle safe lane-changing model. The model considers the priority scheduling problem of different vehicles’ driving behavior when changing lanes, the influence of driver’s subjective factors on the driving speed when changing lanes, and the relationship between vehicle speed and safe lane-changing distance. After discussion and analysis, the model can reduce the number of lane changes of vehicles, increase the average speed of vehicles, and increase the traffic flow. It provides theoretical support for the safe lane-changing behavior of intelligent networked vehicles in the new era.