In this paper, a residual differential pulse code modulation (RDPCM) coding technique using a weighted linear combination of neighboring residual samples is proposed to provide coding efficiency in the screen content video coding. The RDPCM performs the sample-based prediction of residue to reduce spatial redundancies. The proposed method uses the$l_1$optimization in the weight derivation by considering the statistical characteristics of graphical components in videos in an intracoding. Specifically we use the least absolute shrinkage and selection operator to derive the weights because the solution is accurate in high variance residue. Furthermore, we enhance parallelism in a line processing by restricting the support to the row-wise prediction to above samples or the column-wise prediction to the left samples. The proposed method uses an explicit RDPCM scheme, so a coding mode determined by rate-distortion optimization is transmitted to a decoder. For coding the overhead, we develop a context design in CABAC based on correlation between an intraprediction direction and an RDPCM prediction mode. It is demonstrated with the experimental results that the proposed method provides a significant coding gain over the state-of-the-art reference codec for screen content video coding.