There are usually two components in computer screen images: textual and pictorial parts. The pictorial part can be compressed efficiently by classical coding approaches (e.g. JPEG, JPEG2000), while the compression of the textual part is still far away from being satisfactory for the reason that the textual content is usually of high-frequency. In this paper, a learning approach is used to construct a tailored dictionary for text representation. Based on the learned dictionary, a novel screen image compression algorithm is proposed through adopting different basis functions for the textual and pictorial components respectively. The screen images are firstly segmented into textual and pictorial parts. Then we employ traditional discrete cosine transformation (DCT) to facilitate the compression of pictorial part, while the learned dictionary is used to represent the textual part in screen images. Experimental results demonstrate the effectiveness of the proposed compression algorithm.