In order to catch the escaping vehicle quickly with minimum cost, the dynamic containment problem of the target vehicle is studied by using convex hull and graph theory. The police scheduling problem is transformed into a weighted bipartite graph matching problem, and the result of police scheduling with the least time is obtained. Finally, a specific containment scheme is formed, and the improved fast convex hull algorithm combined with the police scheduling algorithm can complete the containment of the escaping vehicles in a relatively short time