The two-stage logistics service supply chain with one logistics service integrator and two functional logistics service providers is considered The decision-making process of the two actors in the logistics service supply chain is modeled as a Stackelberg leader-follower game model and the supply chain contract choice problem of the functional logistics service providers is analyzed In the Stackelberg game, logistics service integrator as the leader determines logistics service price, each functional logistics service providers as the follower chooses either a wholesale price contract or a revenue-sharing contract with the logistics service integrator, and determines the contract parameters, to obtain higher division ratio of the logistics capacity from the logistics service integrator The results show that: in the two-stage logistics service supply chain dominated by the logistics service integrator, the equilibrium is achieved when: 1) two functional logistics service providers choose the same contract, or 2) the functional service provider with lower cost chooses the wholesale price contract and another chooses the revenue-sharing contract No matter which Nash equilibrium strategy is adopted, the logistics service integrator and the functional logistics service providers obtain the same profit So, the revenue sharing mechanism does not outperform than the wholesale price mechanism