A multi-goal multi-agent path planning algorithm was proposed to realize the efficient assignment of tasks to each agent and plan the shortest possible paths for the agents without collision with other agents. The definition of conflict between agents in continuous time and the way of conflict resolution were defined, and the concepts of safety interval and labeling were introduced based on A* algorithm aiming at the problem of low success rate due to the use of discrete time in traditional path planning algorithms. Then the A* algorithm can plan optimal paths that satisfy continuous time constraints. A conflict hierarchical strategy was proposed to reduce the number of nodes extended in the algorithm solving process aiming at the large amount of computation caused by collision detection and conflict avoidance in the multi-agent path planning problem. The experimental results show that the proposed algorithm can solve a better solution and has better applicability, with lower total path cost and higher success rate in the scenario of densely distributed agents.