In this paper, we consider a cooperative autonomous driving system where a vehicle overtakes the one in front based on collective perception. To avoid collisions with vehicles on the other lane, we propose a V2X-based cooperative collision avoidance scheme. The overtaking vehicle estimates the distance between itself and the neighbors via V2V communications and decides whether to overtake or not. Two cases where the distance information is obtained independently and cooperatively are taken into account. We derive the probability of collision avoidance and analyze the influence of different factors such as speed and density of vehicles on the system performance. Simulation results verify our analysis and show that our V2X-based cooperative collision avoidance scheme performs better than traditional GNSS-based collision avoidance scheme. The performance gain brought by the cooperative case compared to the independent case in our scheme can also be observed.