High-speed rail (HSR) systems potentially provide a more efficient way of door-to-door transportation than airplane. However, they also pose unprecedented challenges in delivering seamless Internet service for on-board passengers. In this paper, we conduct a large-scale active-passive measurement study of TCP performance over LTE on HSR. Our measurement targets the HSR routes in China operating at above 300 km/h. We performed extensive data collection through both controlled setting and passive monitoring, obtaining 1732.9 GB data collected over 135719 km of trips. Leveraging such a unique dataset, we measure important performance metrics such as TCP goodput, latency, loss rate, as well as key characteristics of TCP flows, application breakdown, and users' behaviors. We further quantitatively study the impact of frequent cellular handover on HSR networking performance, and conduct in-depth examination of the performance of two widely deployed transport-layer protocols: TCP CUBIC and TCP BBR. Our findings reveal the performance of today's commercial HSR networks “in the wild”, as well as identify several performance inefficiencies, which motivate us to design a simple yet effective congestion control algorithm based on BBR to further boost the throughput by up to 36.5%. They together highlight the need to develop dedicated protocol mechanisms that are friendly to extreme mobility.