In this paper, a novel pyramid coding based rate control scheme is proposed for video streaming applications constrained by a constant channel bandwidth. To achieve the target bit rate with the best quality, the initial quantization parameter (QP) is determined by the average spatio-temporal complexity of the sequence, its resolution and the target bit rate. Simple linear estimation models are then used to predict the number of bits that would be necessary to encode a frame for a given complexity and QP. The experimental results demonstrate that the proposed rate control scheme significantly outperforms the existing rate control scheme in the Joint Model (JM) reference software in terms of Peak Signal to Noise Ratio (PSNR) and consistent perceptual visual quality while achieving the target bit rate. Finally, the proposed scheme is validated through experimental evaluation over a miniature test-bed.