<p>Distributed learning is an effective method for solving large-scale cognitively inspired online machine learning problems. However, frequent communications between nodes lead to expensive communication burden. Meanwhile, projection operations because of the constraints in decision variables cause a lot of computational cost. In order to address the above problems, this paper presents a communication-efficient distributed Frank-Wolfe online optimization method, which integrates the event-triggered mechanism into the distributed projection-free online optimization algorithm. Furthermore, we provide a rigorous theoretical analysis for the regret of the proposed algorithm. Finally, we verify the performance of the proposed method through a variety of numerical experiments. The theoretical results show that the regret reaches a sublinear growth of iterations for convex objective functions. The proposed algorithm outperforms the baseline methods on two datasets. Our research indicates that, in addition to reducing computational overhead, the event-triggered scheme has the potential to enhance the communication efficiency of distributed network system.</p>