Versatile Video Coding (VVC/H.266) greatly improves the compression performance at the cost of extremely high computational complexity compared with High Efficiency Video Coding (HEVC/H.265). Within the context of mobile devices with limited power and computational capabilities, reductions on encoding complexity are important; particularly to encode new data formats such as screen content sequences. Therefore, in this paper, aimed at two brand-new techniques with high complexity, matrix-weighted intra-prediction (MIP) and intra-sub-partition (ISP), we propose a fast intra-prediction scheme for VVC screen content coding based on ultra-lightweight convolutional neural network (CNN). Firstly, an ultra-lightweight CNN is designed to segment the image into the natural content region (NCR) and the screen content region (SCR). Then, an adaptive intra-coding mode pruning scheme based on the ultra-lightweight CNN is proposed to accelerate the VVC screen content coding process. Finally, our proposed method was implemented into VTM-10.0 and experimental results show that our method can save averagely 7.68% and maximum to 13.62% of the encoding time without encoding performance loss.