This paper develops a stop line aided cooperative positioning framework for connected vehicles, which creatively utilizes the location of the stop-line to achieve the positioning enhancement for a vehicular ad-hoc network (VANET) in intersection scenarios via Vehicle-to-Vehicle (V2V) communication. Firstly, a self-positioning correction scheme for the first stopped vehicle is presented, which applied the stop line information as benchmarks to correct the GNSS/INS positioning results. Then, the local observations of each vehicle are fused with the position estimates of other vehicles and the inter-vehicle distance measurements by using an extended Kalman filter (EKF). In this way, the benefits of the first stopped vehicle are extended to the whole VANET. Such a cooperative inertial navigation (CIN) framework can greatly improve the positioning performance of the VANET. Finally, experiments in Beijing show the effectiveness of the proposed stop line aided cooperative positioning framework.