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We frame the collision avoidance problem of multi-agent autonomous vehicle systems into an online convex optimization problem of minimizing certain aggregate cost over the time horizon. We then propose a distributed real-time collision avoidance algorithm based on the online gradient algorithm for solving the resulting online convex optimization problem. We characterize the performance of the algorithm with respect to a static offline optimization, and show that, by choosing proper stepsizes, the upper bound on the performance gap scales sublinearly in time. The numerical experiment shows that the proposed algorithm can achieve better collision avoidance performance than the existing Optimal Reciprocal Collision Avoidance (ORCA) algorithm, due to less aggressive velocity updates that can better prevent the collision in the long run.