Additive manufacturing has emerged as an integral part of modern manufacturing because of its unique capabilities for rapid prototyping and the design flexibility. In order to take full advantage of additive manufacturing, Design for Additive Manufacturing (DfAM) has risen to provide design frameworks, methodologies, and a set of guidelines for effective product designs under additive manufacturing. However, the existing DfAM methods have limitations in that most methods rely on either too general or too specific design requirements and parameters for additive manufacturing; an effective design framework that can consider the capabilities and constraints of additive manufacturing at an early design stage is absent in literature. To tackle this issue, this study develops a design methodology that integrates axiomatic design theory and theory of inventive problem solving (TRIZ) with consideration of additive manufacturing environment. This integrated approach is effective because axiomatic design can be used to systemically define and analyze a design problem, while TRIZ can be used to generate innovative solutions for a design problem. A case study is presented to validate the proposed design framework.