Most standard implementations of congestion control method perform poorly in the satellite Internet due to both a high bit error rate and a long propagation delay. This paper proposes a new TCP congestion control method called TCP-STAR to improve both TCP performance and adaptability of network conditions over the satellite Internet. The performance and the adaptability of network conditions are most important metrics for assurance. TCP-STAR has three new mechanisms, namely Congestion Window Setting based on available bandwidth (CWS), LiftWindow Control (LWC), and Acknowledgement Error Notification (AEN). CWS can avoid the reduction of the transmission rate when data losses are caused by bit error. LWC is able to increase the congestion window quickly based on the estimated available bandwidth. AEN can avoid the reduction of the throughput by mis-retransmission of data. The mis-retransmission is caused by ack losses or delay. Simulation experiments show that TCP-STAR improves the throughput comparing with other TCP variants and exhibits the adaptability of network conditions. Furthermore, the fairness of TCP-STAR is better than that of other TCP variants.