Traditional discrete cosine transform (DCT) can only sparsely represent the horizontal and vertical edges in images, and the computation complexity of directional prediction DCT (DPDCT), which is of ability to represent more directions, is much higher. To overcome these shortcomings, the fast directional lapped transforms (FDLT) is proposed, in which the transform is performed on the predefined direction mode and the energy in edges lying across blocks is compacted further. In Comparison with DPDCT, FDLT needs no interpolation. So FDLT can sparsely represent the anisotropic edges in images much faster. Furthermore, special lifting algorithm is designed to ensure the perfect reconstruction. The computation of FDLT is no more than 2 times of DCT's. Coding with the same set partition method, PSNR of images compressed with FDLT is 0.5dB higher than that with DCT. FDLT based compression also achieves clearer edges and details in the reconstructed images.