The wavelet transform was adopted as the transform for JPEG2000. However, wavelet has weakness about smoothness along the contours and limited directional information. So we use to other transform, called contourlet transform in compression. Objective quality assessment methods currently used Peak signal to noise Ratio(PSNR). But that is not very well matched to perceived visual quality. So new image quality assessment is required. In this paper, we propose a new method for image compression based on the contourlet transform, which has been recently introduced. In addition we evaluated compression image quality using PSNR and SSIM. Finally contourlet transform has a good result about images with smooth contours and SSIM is good method for image evaluation compared to PSNR.