In recent years, the streaming video applications have led to a huge market. But dynamic behavior of the IP network's transmitting bandwidth makes it difficult to provide perceptually good quality of streaming video. The recent technologies of FGS and SVC video coding are proposed to deal with these problems by distributing the data in enhancement layers over a wide range of bit rates. However, data rate of the FGS video coding exhibits significant variability. This variability is meanwhile faced with the problem of the available network bandwidth variability. Therefore, the streaming is faced with the problem of trying to accommodate the mismatch caused by both the available bandwidth variability and the encoded video variability. By using the technologies of prefetching and buffing, this paper focuses on how many encoded video bits of the FGS video should be truncated, and how to truncate them when network available bandwidth isn't enough firstly. Then a scheme of the bandwidth adaptation video transmitting is developed through minimizing to truncate the encoded video bits, and the amount of truncated video bits are analyzed, which can achieve the minimum result theoretically. The scheme can provide a platform of how to compute truncating bit amount for other analogous algorithms. Finally, experimental results show the scheme is efficient and feasible.