Owing to the imminent fixed mobile convergence, Internet applications are frequently accessed through mobile nodes. However, service delivery latency is too high to satisfy user expectations. In this paper, we design a new TCP algorithm, TCP-ME (Mobile Edge), to accelerate the service delivery in mobile networks. Considering the QoS (Quality of Service) mechanisms of mobile networks, TCP-ME is designed to differentiate the packet loss caused by wireless errors, traffic conditioning of mobile core networks, and Internet congestion, as well as to react to the packet loss accordingly. To detect wireless errors, we mark the ACK (Acknowledge) packets in the uplink direction at the base station, and the marking threshold is a function of the instantaneous downlink queue length and the number of consecutive HARQ retransmissions. We modify the ECN mechanism with deterministic marking to detect Internet congestion. The packet loss caused by traffic conditioners of mobile networks is detected by whether the incoming DUPACK is marked or not. TCP-ME adapts the inter-packet interval when the packet loss is caused by wireless errors or the admission control mechanism. If the packet loss is due to Internet congestion, TCP-ME applies the TCP-New Reno's congestion window adaptation algorithm. Simulation results show that TCP-ME can speed up web service response time in mobile networks by about 80%.