In this paper, we present a new post-processing algorithm, based on the theory of projections onto convex sets (POCS), to enhance the quality of decoded images degraded by the blocking artifact. In our approach, by introducing the notion of the global slope, block slope and local slope, a novel linear projection operator is induced. The operator makes the block slopes of two adjacent blocks be equal to the global slope, to alleviate the blocking artifact, while maintaining the local slopes inside the blocks, to preserve most original high frequency components. Computer simulation results on still and moving images show that in the viewpoint of the objective and the subjective quality, the proposed algorithm makes decoded images converge without iteration to the post-processed images, in which the blocking artifact is alleviated effectively, while the conventional algorithms based on the POCS converge with a number of iterations.