Additive manufacturing has emerged as an integral part of modern manufacturing because of its unique capabilities and has already found its application in various domains like aerospace, automotive, medicine and architecture. In order to take the full advantage of this breakthrough manufacturing technology, it is imperative that practical design frameworks or methodologies are developed and consequently, Design for Additive Manufacturing (DfAM) has risen to provide a set of guidelines during the product design process. The existing DfAM methods have certain limitations in that the additive manufacturing process capabilities are not taken into consideration in the early design stage effectively and most of them rely on direct application of existing methods for conventional manufacturing. Furthermore, there is a lack of DfAM methods suitable for additive manufacturing novices. To tackle these issues, this study develops a design framework for additive manufacturing through the integration of axiomatic design approach and theory of inventive problem-solving (TRIZ) with the consideration of additive manufacturing environment. This integrated approach is effective because axiomatic design approach can be used to systematically define and analyze the problem, while the inverse problem-solving approach of TRIZ combined with an additive manufacturing database can be used as an idea generation tool that can generate innovative solutions. Finally, two case studies are presented to validate the proposed design framework.