To unravel the complex challenges addressed by product innovation, it is oftentimes essential for users to participate in the design process. However, there is a paucity of research in terms of in-depth exploration of the cognitive patterns and dynamic design processes of co-design with user participation in the existing design cognition research. The current study aimed to investigate the cognition activities involved in the process of co-design between user and designer at both the individual and team levels. The combination method of linkography and the situated function–behavior–structure (FBS) co-design model was carried out to encode and analyze the protocol data. The results showed that, at the individual level, designers and users adopted different design strategies to promote the progress of the design. In addition, the interaction activities among users and designers varied in different co-design processes. However, at the team level, the collaborators showed systematic thinking modes, and each design move was two-way. This cognitive strategy of the innovation team ensured the continuity and effectiveness of the co-design process. Theoretically, these findings will bring new insights for studies on team cognition activities and contribute to building user-centric design theory by uncovering the dynamic design processes of co-design with user participatory. In addition, the study makes a methodological contribution by illustrating how linkography and the situated FBS co-design model can be utilized to analyze the team cognition during co-design activities.