As the 5G systems have introduced network slicing on the virtualized network environment, application-specific QoS (Quality of Service) management has come to the fore to support a range of services, such as eMBB (enhanced Mobile Broadband), URLLC (Ultra-Reliable Low Latency Communications), and mIoT (massive Internet of Things). It is expected for the next-generation systems to support more diverse applications demanding newer and granular quality characteristics for network services. Most of the current transport layer protocols, built on layering design and best-effort paradigm, do not provide the necessary precision and adaptability required for various QoS support. Therefore, we need new protocols that comprehend application behaviours and adapt to dynamic network conditions for more fine-grained QoS enhancement. This paper presents a Context-oriented Transport (CoT) layer for the next-generation network that understands the application context and adapts to varying network conditions with flowbased QoS control. CoT is an end-to-end software solution that improves the underlying network capacity utilization and prioritizes the traffic flows according to quality needs. We prototyped CoT in Linux/Android devices and evaluated the performance with emulated traffic environment. The experiments show that CoT reduces latency by up to 16.5% and improves average throughput by up to 30%, compared with Android 10 in LTE network, resulting from enhanced traffic classification and network utilization.