The block discrete cosine transform (BDCT) is the most widely used technique for the compression of both still and moving images, a major problem related with the BDCT techniques is that the decoded images, especially at low bit rate, exhibit visually annoying blocking effects. In this paper, based on Mallets multiscale edge detection, we proposed an efficient deblocking algorithm to further improved the coding performance. The advantage of our algorithm is that it can efficiently preserve texture structure in the original decompressed images. Our method is similar to that of Z. Xiong's, where the Z.Xiong's method is not suitable for images with a large portion of texture; for instance, the Barbara Image. The difference of our method and the Z.Xiong's is that our method adopted a new thresholding scheme for multi-scale edge detection instead of exploiting cross-scale correlation for edge detection. Numerical experiment results show that our scheme not only outperforms Z.Xiong's for various images in the case of the same computational complexity, but also preserve texture structure in the decompressed images at the same time. Compared with the best iterative-based method (POCS) reported in the literature, our algorithm can achieve the same peak signal-to-noise ratio (PSNR) improvement and give visually very pleasing images as well.