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A logistics service integrator (LSI) usually requires a logistics service provider (LSP) to carry out smart transformation in order to improve the level of logistics service. However, LSP’s smart transformation faces uncertainty in terms of investments and income, which seriously hinders LSP’s enthusiasm for logistics service innovation. In this paper, we construct a logistics service supply chain (LSSC) consisting of an LSI and an LSP to explore the incentive mechanism for LSPs to undergo smart transformation. As a benchmark for comparison, we first obtain the equilibrium results under centralized decision making and wholesale price (WP) contracts. Then, cost-sharing (CS), revenue-sharing (RS), and cost sharing–revenue sharing (CS-RS) hybrid contracts are proposed. It is found that when the CS coefficient is in a certain interval, the CS contract can increase the profit of LSI and the smart level of logistics service, but it will decrease the profit of LSP. With the exception that the wholesale price of logistics services will decrease, the equilibrium results under the RS contract and WP contract remain consistent. Only the CS-RS hybrid contract can achieve the perfect coordination of LSSC. In addition, by conducting numerical analysis, we find that the enhancement of the smart effect can encourage LSP to improve the smart level and increase the overall revenue of LSSC. To the best of our knowledge, this paper is the first study to explore the incentive mechanism between LSI and LSP in the context of logistics service smart transformation. Our findings guide the LSI in implementing an effective contract.