Most community detection algorithms require the global information of the networks. However, for large scale complex networks, the global information is often expensive and even impossible to obtain. Therefore, local community detection is of tremendous significance. In this paper, a new local community detection algorithm based on NGC nodes, named LCDNN, is proposed. For any node, its NGC node refers to the nearest node with greater centrality. In the LCDNN, local community C initially consists of the given node, v. Then, the remaining nodes are added to the local community one by one, and the added node should satisfy: 1) its NGC node is in C, or it is the NGC node of the center node of C; and 2) the fuzzy relation between the node and its NGC node is the largest; 3) the fuzzy relation is no less than half of the average fuzzy relation of the current local network. The experimental results on ten real-world and synthetic networks demonstrate that LCDNN is effective and highly competitive. Concurrently, LCDNN can also be extended for multiscale local community detection, and experimental results are provided to demonstrate its effectiveness.