Abstract: Be aimed at problems of local community discovery algorithm, such as, it is difficult to obtain the complete information of networks, the existing algorithms have low stability, and it is difficult to set thresholds, etc. We proposes a local extended community discovery algorithm based on boundary nodes (LEAB). Firstly, we select the node with lowest degree in the network, and merge it to the neighbor node which has the most attractive point among its neighbors to establish the initial community. Then, we extend current community with fitness function that determines who can join the initial community from the adjacent nodes set. Finally, repeating above steps we can get the final community discovery result of the network. Compared to existing classical algorithms in artificial networks and real networks, the proposed algorithm has higher accuracy and stability than that of others.