In this paper, we propose a constant quality rate allocation algorithm for MPEG-4 FGS (fine granularity scalability) coded video sequences. The rate allocation problem is formulated as a constrained minimization of quality fluctuation. The minimization is solved using a novel composite rate distortion analysis. For a set of video frames, a composite rate distortion curve is first computed and then used for computing the optimal rate allocation. The proposed algorithm is very efficient because it is neither iterative nor recursive. In addition, after the composite rate distortion curve is computed, it can be used to calculate optimal rate allocation for any rate budget. Therefore, it is suitable for FGS coded bitstreams, which need to be transmitted and decoded many times at many different rates. Moreover, the composite rate distortion curve can be updated efficiently over sliding windows. This further reduces the computational complexity. Experiments using both synthetic and real FGS coded videos have shown the effectiveness and the efficiency of the proposed algorithm.