The development of cooperative relationships among project participants makes relationship norms an important governance mechanism to promote cooperative behavior. However, the research on relationship norms mostly ignored the project network environment established by project participants. A static project network cannot accurately reflect the actual project network state from the perspective of network embeddedness, but the research on the mechanism of cooperative behavior from the perspective of dynamic network embeddedness is limited. Therefore, this study overcame the limitation of static analysis. This paper divided the implementation process of construction projects into early, middle, and late phases. The theoretical model of network embeddedness, relationship norms, and cooperative behavior was tested using sample data from 716 surveys regarding the three phases from China to determine the mechanism of the effect of network embeddedness on cooperative behavior. The research results show that network embeddedness (including structural embeddedness and relational embeddedness) has a direct impact on cooperative behavior. The results also indicate that network embeddedness has an indirect impact on cooperative behavior through relationship norms. Additionally, the results further indicate that the direct and indirect effects of network embeddedness on cooperative behavior are different in different phases of construction projects. With the advance of construction projects, the influence of relational embeddedness increases, whereas the effect of structural embeddedness decreases. The research results deepen the understanding of relationship norms in construction projects and make up for the lack of research on cooperative behavior in construction projects from the perspective of dynamic networks. The research results also provide enlightenment for project participants to fully utilize the network relationships in different phases of construction projects, stimulate the establishment of relationship norms, and promote cooperation. This is helpful to improve the cooperative construction management mode.