The traditional discrete cosine transform (DCT) can only sparsely represent the horizontal and vertical edges in images. The computation complexity of directional prediction DCT (DPDCT), which has the ability to represent more directions, is much higher. To overcome these shortcomings, the fast directional discrete cosine transforms (FDDCT) is proposed in this paper, in which the transformation is performed on the predefined direction mode. Compared with DPDCT, no interpolation is needed in FDDCT, so FDDCT can sparsely represent the anisotropic edges in much faster images. A special lifting algorithm is designed between adjacent blocks to ensure the perfect reconstruction, which compacts energy in edges lying across the blocks. The experimental results show that the computation of FDDCT is no more than 1.4 times that of DCT’s. Coding with the same set partition method, PSNR compressed images that are combined with FDDCT are 0.4~1.6dB higher than those with DCT and DPDCT. Also, the edges and the details in the images are much clearer and less distortion exists.