Under the development of intelligent network technology, drivers can obtain the surrounding traffic situation in real time, which is conducive to improving the stability of traffic flow. Therefore, this paper proposes a new curve-car-following model considering multi-vehicle information of adjacent lanes in connected environment, and conducts linear and nonlinear stability analyses of the model to demonstrate the effectiveness of the proposed model and its ability to improve the stability of traffic system; in addition, numerical simulation experiments of traffic flow convoys are designed to analyze the effects of different parameters in the proposed model on the stability of the traffic flow and test the proposed model’s ability to maintain the following behavior in a convoy. Furthermore, numerical simulation experiments are designed to analyze the effects of different parameters in the proposed model on the stability of traffic flow, and to test the ability of the proposed model to maintain the following behavior in the convoy. The model can provide theoretical guidance to alleviate traffic congestion and improve safety, and extend the application of the following model in curved multi-lane road scenarios.