Block-based compression causes severe pseudo structures. We find that the pseudo structures of images compressed by different levels show some degree of similarity. So we propose to evaluate the quality of compressed images via the similarity between pseudo structures of two images. To obtain a 'reference' image, we introduce the most distorted image (MDI), which is derived from the distorted image and suffers from the highest degree of compression. The proposed pseudo structural similarity (PSS) model calculates the similarity between pseudo structures of the distorted image and MDI. Pseudo structures of the distorted image become similar to the MDI's under the condition of severe compression. Via comparative tests, the proposed PSS model, on one hand, is shown to be comparable to state-of-the-art competitors, and on the other hand, it is not only good at assessing natural scene images but also performs the best in the hotly-researched screen content image (SCI) database. It deserves to mention that PSS is able to boost the performance of mainstream general-purpose no-reference (NR) quality measures.