Image quality assessment (IQA) is widely used in image transmission, processing, and storage, which has important application value. To obtain an IQA model with the excellent performance, combining with the image content features and human visual system characteristics, based on the contrast definition in visual psychology, an IQA method and its mathematical model are proposed. In this method, first based on the contrast definition, combining with the visual characteristics, the contrast between the distorted image and the reference image is used to describe the difference between them; further, based on the difference, a definition method for image quality is proposed. Second, based on the gray and gradient co-occurrence matrix, a concept, which is called as the image gray-gradient expectation (GGE), is proposed, and its calculation method is also illustrated. And based on the GGE values and local contrast of image, a method for describing the image content and its visual perception is proposed. Finally, based on the image content features and the proposed definition method of image quality, an IQA method and its mathematical model are proposed. Further, they were tested using the 142 reference images and 7220 distorted images in the LIVE, CSIQ, TID2008, TID2013, CIDIQ, and IVC databases. And the results were compared with those of seven existing typical IQA models in terms of accuracy, complexity, and generalization performance. These experimental results show that, in the six databases, the IQA accuracy Pearson linear correlation coefficient of the proposed model can all be more than 0.7892 and reach 0.9638 highest, whose comprehensive efficiency is better than ones of the seven existing IQA models. These analysis and comparison show that the proposed model is an excellent IQA model on performance.