Compared with the address-centric network such as the Internet, the content-centric networking (CCN) has a potential advantage in terms of content-centric communications and could be an ideal solution to achieving content-centric communications in mobile networks. However, CCN depends on broadcasting and reverse paths to achieve content-centric communications, so it suffers from the heavy content communication cost and the frequent content communication failure. In this paper, we propose a CCN for mobile networks with the Internet environment and aim to take advantage of the advantages of the address-centric network and CCN to reduce the content communication cost and improve the content communication success rate. In this proposal, a consumer achieves content-centric communications in the address-centric unicast way without depending on reverse paths. Moreover, a consumer can acquire contents from any optimal provider with target contents rather than a specific provider identified by a destination address. Finally, this scheme is analyzed and evaluated, and the data show that it effectively reduces the content communication cost and improves the success rate.