In this paper, the problem of online distributed optimization is investigated, where the sum of locally dynamic cost functions is considered to be strongly pseudoconvex. To address this problem, we propose an online distributed algorithm based on an auxiliary optimization strategy. The algorithm involves each agent minimizing its own cost function subject to a common convex set while exchanging local information with others under a time-varying directed communication graph sequence. The dynamic regret is employed to measure performance of the algorithm. Under mild conditions on the graph, it is shown that if the increasing rate of minimizer sequence & x0027;s deviation is within a certain range, then the bound of each dynamic regret function grows sublinearly. Simulations are presented to demonstrate the effectiveness of our theoretical results.