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TCP Vegas is supportive to space communication. However, the performance degrades when it is used in LEO satellite networks. The handover and rerouting issues in LEO satellite networks cause path change and abrupt delay variance. The congestion window size should be increased when delay increases due to path change, but TCP Vegas reduces the window size by mistake, and the throughput degrades. In this paper, the behavior of TCP Vegas in LEO satellite network is studied. A method is proposed for correctly adjusting the congestion window when the path changes. Simulation results show that the method is validity and the performance of TCP Vegas is improved.