With the increasing utilization of High-Speed Trains (HSTs), the need for a reliable and high-bandwidth Internet access under high-speed mobility scenarios has become more demanding. In static, walking, and low mobility environments, TCP/IP (transmission control protocol/Internet protocol) can work well. However, TCP/IP cannot work well in high-speed scenarios because of reliability and handoff delay problems. This is mainly because the mobile node is required to maintain the connection to the corresponding node when it handovers to another access point node. In this paper, we propose a named data networking wireless mesh network architecture for HST wireless communication (NDN-Mesh-T), which combines the advantages of Wireless Mesh Networks (WMNs) and NDN architectures. We attempt to solve the reliability and handoff delay problems to enable high bandwidth and low latency in Internet access in HST scenarios. To further improve reliability and bandwidth utilization, we propose a Direction-Aware Forwarding (DAF) strategy to forward Interest packet along the direction of the running train. The simulation results show that the proposed scheme can significantly reduce the packet loss rate by up to 51% compared to TCP/IP network architecture. Moreover, the proposed mechanism can reduce the network load, handoff delay, and data redundancy.