Detecting community structure/modules in complex networks recently attracts increasing attention from various fields including mathematics, physics and biology. In this paper, we propose a method based on graph-theoretical clustering for identifying modularity structure in complex networks. Compared with the existing algorithms, this method, based on minimum spanning tree, has several advantages. For example, unlike many algorithms, this method is deterministic and not sensitive to the initialization. In addition, the method does not require a prior knowledge about the number of the modules. It can easily obtain the number of clusters by analyzing the edge weight distribution of minimum spanning tree. Moreover, this algorithm has computational compexity of polynomial-time with low order and can be used to deal with large-scale networks. Experimental results show that our method produces good results for real networks and can also uncover meaningful functional modules in protein interaction networks.