The components of the logistics and supply chain are analysed to meet the needs of supply chain management and decision support, aiming at the complexity and uncertainty of the supply chain system. First, the characteristics of logistics demand and logistics service types of some enterprises are analysed. The factors affecting supplier selection are obtained through the questionnaire survey of some enterprises. Second, the mutual feedback relationship between the influencing factors of logistics service demand is analysed, and a fuzzy cognitive graph model of the selection process of enterprise logistics service providers is established. Finally, the fuzzy cognitive map (FCM) model is used to conduct an empirical study on the choice of logistics service providers. The results show that the ranking results of the three candidate logistics service companies based on FCM are WL1 (0.7233) > WL3 (0.6823) > WL2 (0.6764). When each node of the concept does not affect each other, the ranking result of the three candidate logistics service companies based on analytic hierarchy process (AHP) is WL1 (0.7265) > WL2 (0.6949) > WL3 (0.6920). The final evaluation result will be affected by the mutual influence relationship between the concept nodes. Overall, the lowest evaluation score is WL2, and the highest is WL1. The most suitable logistics service provider for the enterprise is WL1. The FCM model selected by the manufacturing enterprise logistics service provider is reasonable and feasible. The mutual feedback between evaluation factors affects the selection of logistics service providers in a company. The FCM can get a more accurate evaluation weight value and can realize the optimal choice of logistics suppliers. It provides reference and decision support for other enterprises.