In construction projects, cost-related risks are challenges that need to be coped with. These cost-related risks interact with each other along with the project progress and involve different stakeholders, forming a stakeholder-cost risk network. Previous studies have discussed the stakeholder-cost risk network; however, few studies have considered its dynamic characteristics. Different from traditional methods, this study employed the social network analysis (SNA) to explore the key indicators of cost-related risks within the supply chain and identify the key risks and stakeholders across four project stages: the planning start-up stage, design preparation stage, construction period, and operations and maintenance period. From a horizontal point of view (i.e., network development process), the complexity of the stakeholder-cost risk network demonstrates a U-shaped development process during the project life cycle, ranging from simple to complex to simple. From a vertical point of view (i.e., network hierarchical characteristics), the important cost-based risks are diversified within each stage. The current study contributes to forming a better understanding of the stakeholder-cost risk network from a dynamic perspective as well as the crucial cost-based risks within each stage of the project. The findings provide implications for managers to better align cost-based risk intervention strategies, thereby facilitating the achievement of construction project success.