A method of constructing and maintaining a circle-mesh overlay network is disclosed. The method of constructing a circle-mesh overlay network includes: (a) determining a reference member number of a circle overlay by using a total number of participating peers; (b) creating a new circle overlay and adding member peers from among the participating peers to the new circle overlay in consideration of the reference member number; and (c) forming a circle-mesh overlay network by way of interconnection between the new circle overlay and a different circle overlay.