Wireless channel contention/interference problems combined with the constraints imposed by the TCP congestion control scheme have a severe impact on TCP throughput performance and fairness in a wireless mesh network. In this paper, we propose a TCPsleek spatial TDMA scheduling algorithm to construct a sleek data and ACK packet flowing environment for TCP flows along the wireless paths. The proposed scheme considers the TCP demands of individual directional links during channel access scheduling and time slot assignment to enable the TCP congestion control mechanisms to perform as effectively as they do in wired networks, irrespective of their spatial locations and the number of hops traversed. In addition, employing link-layer retransmission can effectively hide local transmission errors from the end-to-end TCP congestion control mechanisms. The simulation results demonstrate that, under the proposed scheme, the problem of unfair bandwidth sharing to long-hop TCP flows caused by wireless communication is successfully eliminated, and the throughput disparity between long- and short-hop TCP flows is also substantially reduced. The scheme also achieves high overall network throughput.