In order to improve TCP performance in networks with large round trip time, a method using a PEP (Performance Enhancing Proxy) is a proposed. In the method, the PEP is located on a intermediate router along a TCP connection, and returns acknowlegdment packets (premture ACKs) to the source host instead of the destination host. In previous researches, although a congestion control in the PEP which keeps the number of prematurely acknowledged packets below a threshold (watermark) value has been proposed, packet losses are not taken into account. In this paper, we incorporate a retransmission control to deal with packet losses into the congestion control. the proposed retransmission control mainly has two functions. One is to return duplicate premature ACKs to solicit the fast retransmission in the source host, and the other is to retransmit packets by timeouts and receive of duplicate acknowledgments from the destination host. In addition, TCP selective acknowledgment (SACK) option is supported in the PEP. If the source host can treat the option, the PEP returns premature ACKs with the option.