This paper firstly models fast retransmission and recovery in TCP selective acknowledgement (SACK). The model of fast retransmission and recovery in TCP SACK is represented by the expected number of packets transmitted during fast retransmission and recovery in TCP SACK and the corresponding expected duration. Then, based on Gilbert model and the model of fast retransmission and recovery, a steady state throughput model (full model) for TCP SACK is modeled and expressed as a function of burst event rate, burst loss rate and average round trip time. Finally, the full model of TCP SACK is validated under one bottleneck scenarios and multiple bottlenecks scenarios with HTTP, FTP and UDP traffics. The results show that the full model estimates the throughput of TCP SACK flow more accurate than TST model under high bandwidth delay product (BDP) networks. Furthermore, the results also indirectly validate the correctness of the fast retransmission and recovery model in TCP SACK and reveal that the smaller the BDP, the less bursty the losses.