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Thousands of bursty and concurrent flows persistently overwhelm the bottleneck bandwidth. The quality of experience of low-latency applications (e.g. Web, AR/VR, IoT, VoIP, etc.) is inevitably influenced by the background applications (e.g. file-sharing, system updates) which tend to overfill the buffer of bottleneck links. To solve the above issues, Less-than-Best-Effort (LBE) protocols were proposed to support the data transmission of background applications. Therein, Low Extra Delay Background Transport (LEDBAT) is one of the most widely deployed LBE protocols. To achieve the low-priority feature, LEDBAT senders saturate the residual bandwidth of bottleneck links while keeping the low queuing delay. However, through the simulation, we observed that LEDBAT performs a severe throughput degradation in high-speed and lossy networks. To resolve this issue, an enhanced LEDBAT, named NLPC, is presented in this paper. NLPC introduces a variable gain value, which can dynamically adapt to the network congestion degree, to update the sending rate. Extensive simulations in NS-2 and some small-scale real-world experiments indicate that in high-speed and lossy networks, NLPC increases throughput up to 40% in comparison with LEDBAT, and maintains the low-priority feature as the other LBE protocols.