In this paper, we propose a Dynamic routing Scheme (DRS) to improve TCP connection throughput on wireless mesh networks (WMN). At first, a RTT-based congestion detection module is developed to identify congestion occurrence by RTT measurement. Then a path-discovery module is developed to establish and maintain an alternative path to deliver the data packet, instead of the congested primary path. Finally, the source will route data packets to the alternative path seamlessly. A series of simulations is conducted to evaluate the performance of the proposed DRS in cases of various traffic interferences. Besides, the impact of the path-switching on throughput is also explored. Experimental results demonstrate that the proposed DRS, in average, enhances TCP connection throughput by 65.75% relative to the connections with traditional static routing, even in the condition of heavy background traffic.