Communities exist in complex networks of different areas, and in some cases they may overlap between each other. Community detection is a good way to understand the structure, function and evolution of complex networks. There have been some methods to find disjoint or overlapping communities. While most of these methods only fit one single situation, disjoint or overlapping. In our opinion, it is unreasonable to find disjoint communities on a network with clear overlap or to find overlapping communities on a network without any visible overlapping node. In this paper, we propose a link partition based method which can find communities with adjustable extent of overlapping according to backgrounds of specific applications or personal preferences. Experimental results on some real-world networks show that our method can find reasonable communities with adjustable extent of overlapping, and is suitable for networks with high densities and large scales.