In this paper, the lossy image compression algorithm using the quad tree and the bandlets is proposed. The proposed algorithm transforms input images by the discrete wavelet transform (DWT) and represents the geometrical structures of high frequency bands using the bandlets with a 8 block- size. In addition, the proposed algorithm searches the position information of the significant coefficients by using the quad tree algorithm and computes the magnitude and the sign information of the significant coefficients by using the Embedded Image Coding using Zerotrees of Wavelet Coefficients (EZW) algorithm. The compression result by using the quad tree algorithm improves the PSNR performance of high frequency images up to 1 dB, compared to that of JPEG-2000 algorithm and that of S+P algorithm. The PSNR performance by using DWT and bandlets improves up to 7.5dB, compared to that by using only DWT.