In TCP over OBS networks, consecutive multiple packet losses are common since an optical burst usually contains a number of consecutive packets from the same TCP sender. In this paper, we first present a new theoretical method to analyze the behavior of Reno when consecutive multiple packet losses occur. Results of the analysis indicate that even a small number of consecutive multiple packet losses can force Reno to timeout. Then we propose B-Reno, a newly designed TCP implementation that can overcome Reno's inefficiency in dealing with consecutive multiple packet losses over OBS networks and can avoid the shortcomings of New-Reno and SACK. Results of comprehensive simulations indicate that B-Reno over OBS networks can achieve a performance better than Reno and New-Reno, and that it can also achieve a performance similar to that of SACK. Moreover, B-Reno only needs some simple modifications to New-Reno at the sender's protocol stack, and thus has less difficulty in deployment and less protocol complexity than that of SACK.