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In cognitive radio (CR) networks, the multichannel access problem is an important problem, which may directly affect user applications. However, most of previous work on this problem focuses on maximizing physical layer throughput, rather than the end-to-end transmission control protocol (TCP) performance. In this paper, we propose an optimal TCP throughput based channel access scheme in CR networks, and the TCP performance is improved from a cross-layer perspective. Specifically, we formulate the channel access process in CR network as a stochastic system. With the stochastic optimization formulation, the optimal channel access policy is indexable, meaning that the channels with highest indices should be selected to transmit TCP traffic. Simulation results show the TCP throughput can be improved substantially compared with the existing approach that maximizes physical layer throughput.