In this paper, we propose a new approach for reducing the blocking artifact that is one of drawbacks of the block-based Discrete Cosine Transform (DCT) without introducing additional information or significant blurring. We modify the inter-block discontinuity minimization technique to preserve edges within a block as well as to reduce visible block boundaries. The homogeneity of each block is decided by the threshold value reated to Q-factor, which is included in a JPEG as well as MPEG streams. The quantization error is estimated by minimizing the discontinuity, which is weighted in proportion to block discontinuity and added to each pixel in the block to compensate block artifacts. The proposed algorithm reconstructs images which have less noticeable block boundaries from a subjective viewpoit without anyconstraints.