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XCP and VCP can achieve excellent performance under high bandwidth-delay product networks, but they all have some defects. In XCP, router needs to calculate a feedback for each departing packet, the cost will be un-negligible in high-speed networks. In VCP, router classifies the degree of congestion into three regions and encodes it in ECN bits to guide sender to update its congestion window (cwnd). Obviously, the feedback in VCP is still not precise enough so that VCP has slow fairness convergence speed. Moreover VCP does not consider the TCP unfairness problem induced by heterogeneous packet sizes. Furthermore, both XCP and VCP cannot solve unfairness problem led by multiple bottleneck routers. To overcome drawbacks in XCP and VCP, we propose a new efficient and fair explicit congestion control protocol in this paper, for convenience, we call it EFXCP. In a sample interval, EFXCP router calculates an expected fair throughput and feedbacks it to senders. EFXCP sender updates its cwnd to make its' throughput converge to expected fair throughput so that the system can rapidly converge to the optimal state. On the one hand, EFXCP calculates feedback only once in a sample interval, the calculation cost is much less than that in XCP. On the other hand, EFXCP adopts the precise feedback, the fairness convergence speed is much faster than that in VCP. Furthermore, one outstanding advantage of EFXCP is that it can achieve excellent fairness in all cases, all competing flows have almost the same throughput when system is stable. Using control theory, we demonstrate that EFXCP is global asymptotic stable regardless of bottleneck capacity, round trip delay time (RTT) and number of sources. Moreover, we quantificationally analyze the rise time and the fairness convergence time of EFXCP. Further, we evaluate the performance of EFXCP using extensive NS2 simulations over a wide range of network scenarios, the results show that EFXCP retains the advantages of XCP and VCP, and discards their disadvantages, and achieves excellent performance. Moreover, like VCP and XCP, the router does not maintain per-flow state.