A novel SAR image compression algorithm was presented by using lifting directionlet transform(LDT). The lifting directionlet scheme and improved quad-tree segmentation were proposed to obtain the optimal pair of transform directions, which could capture the image features efficiently. To enhance the coder performance, multi-directional anisotropy hierarchical zerotree was designed, which was suitable to the distribution characteristic of LDT coefficients. Experimental results of real SAR images show that the proposed compression algorithm outperforms the wavelet-based SPIHT and JPEG2000 both in terms of evaluation metric as well as visual quality, especially at the low-bitrate.