In the paper, we propose a congestion control scheme for reliable multicast communication which enables TCP fairness and prevents a drop-to-zero problem. The proposed congestion control scheme is rate-based one based on NAKs from receivers and cooperatively works with a flow control scheme. The congestion control scheme consists of two components of a rate-based controller and a selection mechanism of a representative. The rate-based controller runs between the sender and the representative and achieves TCP fairness and fast response to losses at the representative. The selection mechanism of the representative allows the sender to select the representative in a scalable manner, in which the sender makes use of NAKs from receivers to select it. In the paper, we also propose the switchover mechanism of the flow and congestion control schemes which enables the sender to use either of them adaptively based on network situations. When the network is congested, the congestion control scheme works to share network resources fairly with competing TCP flows. Otherwise, the flow control scheme works to adapt the transmission rate to the slowest receiver. We verify the performance of our proposed schemes by using computer simulation.