Transport Control Protocol (TCP) has served as a reliable, self-regulated, and congestion tolerant transport protocol for many Internet applications. Relatively, limited knowledge has been gained in terms of the impacts encountered in TCP when Optical Burst Switching (OBS) is adopted in the network backbone. A novel scheme, called TCP with Explicit Notification Generalized Additive Increase Multiplicative Decrease (TCP-ENG), is introduced, which is considered as the first study that integrates the explicit notification platform with the GAIMD approach. The proposed scheme aims to solve the false congestion detection problem in the IP over OBS networks. An analytical model is developed for the proposed scheme and is verified through extensive simulation.