Smooth rate control schemes are necessary for Internet streaming flows to use available bandwidth. To equally share the Internet bandwidth with existing Transmission Control Protocol (TCP) flows, these new schemes should meet TCP-equivalent criterion, i.e., achieve the same transmission rates as TCP under the same network conditions. However, when the available bandwidth oscillates, many of these schemes fail to meet this criterion due to their slow increasing rate. This study proposes a window-averaging rate control (WARC) scheme to send packets at the same average rate as a TCP flow over a fixed time interval. Considering the TCP rate only over a fixed interval allows WARC to forget the historical loss condition more rapidly than other schemes, thus achieving a faster increasing rate when additional bandwidth becomes available. When the available bandwidth drops dramatically, WARC uses a history-reset procedure to converge its rate to the new steady rate immediately after a specified number of losses. The simulations in this study show that WARC not only achieves the same bandwidth as TCP, but exhibits faster convergent behaviors and has a smoother rate than existing schemes.