Transmission Control Protocol (TCP) is still dominant for reliable end-to-end data transmission with congestion control over diverse types of networks although it does not perform well in goodput on lossy networks. To mitigate the goodput degradation of TCP on lossy networks, TCP with Network Coding (TCP/NC) was proposed. But it has not been well deployed because TCP/NC should be implemented in both sides of end-to-end connection; it requires considerable costs and is sometimes difficult in tiny end devices, e.g., with less memory and power. In this paper, to utilize the potential of TCP/NC more practically with no change on end-host TCP, we consider the TCP/NC tunnel that simply conveys end-to-end TCP sessions not only on a single TCP/NC session but also on cascaded TCP/NC sessions traversing a lossy network in the middle without per-session management. The simulation results by Network Simulator 3 clearly show the benefit of the multiply-cascaded TCP/NC tunnel. In congestion scenarios with a wide range of link loss rates, the end-to-end standard TCP with multi-cascaded TCP/NC tunnel can achieve a significantly higher goodput compared to both the end-to-end TCP/NC without tunnel and the end-to-end standard TCP with single TCP/NC tunnel.