Screen content generally consists of text, images, and videos variously generated or captured by computers and other electronic devices. For the purpose of coding such screen content, we introduce alternative intra prediction (AIP) modes based on the emerging high efficiency video coding (HEVC) standard. With text and graphics, edges are much sharper and a large number of corners exist. These properties make it difficult to predict blocks using a one-directional intra prediction mode. The proposed method provides two-directional prediction by combining the existing vertical and horizontal prediction modes. Experiments show that our AIP modes provide an average BD-rate reduction of 2.8% relative to HEVC for general screen contents, and a 0.04% reduction for natural contents.