Digital video's increased popularity has been driven to an extent by a flurry of recently proposed international standards. In most standards, the rate control scheme, which plays an important role for improving and stabilizing the decoding and play-back quality, is usually not defined. Several techniques have been proposed to aim at the best possible quality for a given channel rate and buffer size. These approaches are complex in that they require the R-D characteristics of the input data to be measured. In this paper, we propose a method to approximate the rate and distortion functions to reduce the complexity of the optimization procedures while making a minimal number of a priori assumptions on the source data. In the proposed method, the R-D of image frames is approximated by spline interpolation functions, and inter-frame dependency (for P or B frames in MPEG) are modelled by a linear-constant function. The application to gradient-based rate-control scheme for MPEG shows that, for a typical MPEG encoder, by using the proposed model, the same performance can be achieved with only about 10 to 15 percent of computation cost.