Different problems in the process of product innovation are often caused by external environmental changes of the product. There is a lack of research on classifying the problems associated with product environment changes to aid in applying tools of the Theory of the Solution of Inventive Problems (TRIZ) for problem-solving. This paper proposes a Cynefin framework to classify the problems into disorder, chaotic, complexity, complicated and simple areas according to the external environment changes. Each area of problems is then solved by corresponding design tools in TRIZ. Chaotic and complex problems are converted into complicated or simple areas by the technology evolution and effect search. Complicated or simple areas are combined considering conflicts expressed by an Element-Name-Value (ENV) model. Key conflicts are determined by simplified rules of a node conflict network. A problem-solving methodology in product innovation is proposed based on Cynefin framework-aided TRIZ. The proposed method is applied in the design of an enterprise SJL900/32 mobile bridge erecting machine.