Projects involve inter-organizational relationship cognition, which is central to collaborative engineering project value added. Interest in value added in the project lifecycle is mounting and gaining increasing attention in the research literature. However, little is known about how inter-organizational relationship cognition facilitates value added and how such cognition pushes a project toward higher end-states of value. The existing literature mainly analyzes and studies value added on functional analysis and cost control. There are predominantly static analyses of the factors that influence value added in studies. The guiding role of value added has not been adequately explored in the studies on the influencing factors of value added. Utilizing a combination of Structural Equation Modeling (SEM) and Fuzzy Cognitive Maps (FCMs), this study addresses how inter-organizational relationship cognition influences engineering project value added, identifying complex structures of interaction and cognition dynamics. Results indicate that: (1) A hybrid SEM–FCM method can be able to model dynamic interactions between inter-organizational relationship cognition and value added; (2) trust and shared vision have positive effects on in-role behavior and extra-role behavior. Shared vision has a negative effect on opportunistic behavior. In-role behavior and extra-role behavior have a positive impact on value added, while opportunistic behavior has a negative impact. Organizational behavior is an important mediating variable to explain the interaction between inter-organizational relationship cognitions and value added. This hybrid method explores the potential mechanisms of inter-organizational relationship cognition on project value added from novel perspectives on construction project management practices, proposing practical advice for further project management.