In this study, a novel intentional island model of a distribution system with distributed generations (DGs) is presented and the improved Dijkstra algorithm is used to solve this model. This paper abstracts the distribution network with DGs to the layered directed tree according to its radial structure and power restoration process. In consideration of grade, controllability, capacity, level and electrical betweenness of load, the model weights load and maximizes total load weight in the island. The proposed model considers power balance, node voltage, phase angle and transmission capability of the branch, and network connectivity to meet practical engineering requirements. The improved Dijkstra algorithm formulates a search rule to select the load that can be divided into an island in descending order of the shortest path between the load node and DG node. An optimal island partition scheme is achieved through three stages: origin island, baby island and mature island. Meanwhile, scheme adjustment and constraint checking are used alternately to balance objective functions and constraints. The improved IEEE 43-bus distribution network is applied to verify the validity of the algorithm. A comparison of two island methods shows that the proposed algorithm can generate a reasonable scheme for island partitioning.