To reduce the effects of uncertain material demands on the stability of maritime logistics network in remote islands, this paper investigates the design problem of a three-level hub-and-spoke material distribution network consisting of a mainland supply port, central islands, and satellite islands. The problem is formulated as a location-inventory-routing model that includes decisions on the number of central island locations, aiming to minimize system costs. The model takes into account some practical factors such as heterogeneous fleets, transportation mode diversity, and inventory capacity constraints. An Integrated Genetic-Annealing Optimization Algorithm Embedded with Monte Carlo Simulation-Based Neighborhood Traversal Operators (GAAEMCNT) is developed to decompose the original problem into several sub-problems, including location and assignment, route grouping, and optimization of route and inventory. The integrated optimization of the problem is realized through the interaction and iteration of inner and outer layer of the GAAEMCNT algorithm. Experiments on islands in the South China Sea are conducted to analyze the effects of changes in the number of islands, density distributions and demand on the maritime network system. The results show that: (i) when the distribution of material demand on islands is unchanged and the number of islands is the same, the unit cost of logistics network in the aggregation distribution is lower than that in the discrete distribution; (ii) when the distribution of island material demand is unchanged and the distribution of island is the same, the change of island number has minimum influence on the unit cost of logistics network; (iii) the change of the mean value of the material demands in the islands has a significant impact on the cost of each part of the system, and the total cost is positively correlated with the mean value; (iv) the fluctuation of the demand has a more obvious impact on the cost of the storage system, but a smaller impact on the cost of the transportation system. These findings validate the applicability of the algorithm proposed in this study across various island scenarios, providing decision-making support for the construction and optimization of maritime logistics network in remote islands under demand uncertainty. © 2024 Science Press. All rights reserved.