Abstract: The low-thrust trajectory optimization for the multi-asteroid exploration with time and fuel limits is studied in this paper. The optimal control problem is established based on the minimum principle and is solved by the homotopic approach. The target flyby, the rendezvous and the stay time after the rendezvous are all treated as the inner constraints. Then the global optimal control problem is solved by the homotopic approach. It is shown that the global optimal trajectory can be obtained quickly. The algorithm proposed in this paper can be employed in the mission design and the trajectory optimization for multi-asteroid explorations.