In order to study the theory and application of computer aided design (CAD) related to the composition of art, the theory of symbolic matrix was introduced to realize the purpose of the study of the interaction between perceptual and rational problems. In this paper, the original image was extracted from the design object, and the transformation between the original image and the symbol matrix was realized by the correspondence with the elements in the matrix. Based on the research route, four kinds of mathematical models were established, namely random distribution, symmetric distribution, central diffusion, and reorganization. By applying the mathematical model constructed in this paper, the picture was transformed, the combination of various styles of graphics was added, and how to put the simple image picture into a meaningful integrated image picture was discussed. The computer-aided design method of the existing verification examples was summarized in this paper, and the design method was accurate and effective. Compared with traditional graphic art design methods, the computer-aided design method mentioned in the paper has the following advantages. Computer-aided design can quickly process and analyze images, convert and combine them through mathematical models and algorithms, greatly saving designers time and energy. By introducing symbol matrix theory and establishing various mathematical models, computer-aided design can provide diverse graphic combinations and style transformations, helping designers explore more innovative design solutions.