Reliability is the core indicator for measuring the operational service quality of a logistics distribution network. In order to explore the impact of distribution center inventory on the reliability of logistics distribution network, the logistics distribution network was modeled as multi-state flow network model, and based on the assumption that the inventory in distribution centers was given priority to supply the market and the transportation cost had a limit, network reliability refers to the probability that the commodities transported to a certain market could meet the demand and the total transportation cost did not exceed the given limit. According to the relationship between distribution center inventory and market demand, a reliability evaluation method based on minimal capacity vectors was proposed. The reliability evaluation method is verified by example analysis, and the influence of different inventory combinations on network reliability is analyzed. The results show that increasing distribution center inventory does not always improve network reliability.