In the recent years, researches focus on decay of TCP throughput over wireless links, and many wireless TCP solutions are proposed to deal with this issue. On the other hand, followed by the improvement of hardware technology, new network structures and mechanisms are proposed to enhance wireless communications, for example, the Cognitive Radio (CR) networks. However this new network architecture causes a new problem, which is not solved in wireless TCPs. In this paper, we identify a new issue that impacts the TCP performance over CR networks, which we call Bandwidth Variation. A cross layer solution is proposed to deal with this new issue. Both numerical and simulation results are presented to demonstrate the effectiveness of the proposed solution.