The purpose of this study is to explore the design of equity cooperation mechanism in the sharing logistics service supply chain. This study designs a two-echelon logistics service supply chain composed of an urban joint distribution company and N logistics companies. The urban joint distribution company is jointly established by N logistics companies based on specific shares of equity investment. We establish sharing logistics service supply chain models under revenue-sharing or cost-sharing contracts. Revenue-sharing factor or cost-sharing factor is the equity cooperation parameter. When the members of the supply chain choose to cooperate in revenue-sharing or cost-sharing mechanism, not all cooperation scenarios considered in the study can achieve Pareto improvement of the total profit of the supply chain, but at least one situation can achieve Pareto improvement. This study provides feasible solutions for logistics companies to join the sharing logistics service platform and provides a reference for the operation of a joint distribution platform established by logistics companies. New results and managerial insights are derived by the sharing logistics service supply chain with revenue-sharing vs cost-sharing contracts, which enriches the interfaces of the operation of the sharing logistics service supply chain.