Fine-Granularity-Scalability (FGS) coding can provide the flexibility and good performance for video streaming, and thus has been accepted in MPEG-4 and H.26L. It is noticed that FGS can be truncated anywhere to adapt the changes of the network bandwidth. However, the existing simple truncation methods would lead to the fluctuation of the quality of video sequence. Often, users would like to obtain a smooth quality. Based on the discussions of related works, this paper presents two equal-quality FGS video streaming algorithms with/without loss in the non-real-time streaming application scenarios. These algorithms are based on the piece-wise line R-D model and the slide window protocol. In the lossless case, the bisection method is exploited to allocate the network bandwidth among the frames in the current window so as to realize the equal-quality FGS video streaming; while in the loss case, an adaptive heuristic algorithm and the forward effort correction (FEC) technique are used for the same purpose. The experimental results demonstrate that the algorithms can have good performance in both of the two cases, thereby obtaining the smoother streaming quality of FGS video sequence.