Axiomatic design and design structure matrix (DSM) are two popular design methods at the moment, while most related researches only apply the basic ideas of axiomatic design or DSM to some use cases. This paper analyses the disadvantages of both axiomatic design and DSM. The axiomatic design method guides the designer finding suitable design parameters to meet the needs of function requirements. But axiomatic design cannot support the designer to know the interactions amongst the design parameters, including geometry, spatial layout, interfaces (e.g. logical and physical connectivity), which will decide the quality of the design. DSM has the advantages at recording and analysing the interaction relationship between existing product elements. However, at the conceptual design stage or for a new product that has never been designed before, it is difficult to make the DSM. After deep investigations, it has been found that there are strong complementarities between axiomatic design and DSM, and integration of both sides is advocated for better-quality design. The main outcome of this work is the formal interpretation of the integration logic between axiomatic design and DSM. Under such integration context, the conceptual design process can be seen as a recursive interaction of axiomatic design's design matrix (DM) and corresponding DSM. In this way, axiomatic design and DSM can benefit from each other. A computer-aided conceptual design system has been developed to realize the proposed integration model of axiomatic design and DSM.