In order to find a cover which allows nodes to be shared among several communities, we propose a simple fuzzy community detection algorithm, which is based on an existing partition detection technique. For the performance of overlapping nodes that makes the partition ambiguous, a new extended modularity is introduced to qualify covers. With modularity optimization, the cover can be found with a high quality. We applied our method to real networks. The results demonstrate that our method can discover meaningful fuzzy community structure, overlapping community structure and hierarchical structure.