An island logistics system is vulnerable in emergency conditions and even isolated from land logistics. Drone-based distribution is an emerging solution investigated in this study to transport packages from a land base to the islands. Considering the drone costs, drone landing platforms in islands, and incorporation into the island ground distribution system, this study categorizes the direct, point-to-point, and cyclic bi-stage distribution modes: in the direct mode, the packages are distributed from the drone base station to the customers directly by drones; in the point-to-point mode, the packages are transported to the drone landing platform and then distributed to the customers independently; in the cyclic mode, the packages are distributed from a drone landing platform by a closed route. The modes are formulated, and evaluation metrics and solution methods are developed. In the experiments based on an island case, the models and solution methods are demonstrated, compared, and analyzed. The cyclic bi-stage distribution mode can improve drone flying distance by 50%, and an iterative heuristic algorithm can further improve drone flying distance by 27.8%, and the ground costs by 3.16%, average for the settings of twenty to sixty customers and two to four drone landing platforms. Based on the modeling and experimental studies, managerial implications and possible extensions are discussed.