For MPEG video coding and recording applications, it is important to select quantization parameters at slice and macroblock levels to produce nearly constant quality image for a given bit count budget. A well designed rate control strategy can improve overall image quality for video transmission over a constant-bit-rate channel and fulfill editing requirement of video recording, where a certain number of new pictures are encoded to replace consecutive frames on the storage media using at most the same number of bits. In this paper, we developed a feedback method with a rate-quantization model, which can be adapted to changes in picture activities. The model is used for quantization parameter selection at the frame and slice level. Extra computations needed are modest. Experiments show the accuracy of the model and the effectiveness of the proposed rate control method. A new bit allocation algorithm is then proposed for MPEG video coding.