Storage reliability is an important index of ammunition product quality. It is the core guarantee for the safe use of ammunition and the completion of tasks. In this paper, we develop a prediction model of ammunition storage reliability in the natural storage state where the main affecting factors of ammunition reliability include temperature, humidity, and storage period. A new improved algorithm based on three-stage ant colony optimization (IACO) and BP neural network algorithm is proposed to predict ammunition failure numbers. The reliability of ammunition storage is obtained indirectly by failure numbers. The improved three-stage pheromone updating strategies solve two problems of ant colony algorithm: local minimum and slow convergence. Aiming at the incompleteness of field data, “zero failure” data pretreatment, “inverted hanging” data pretreatment, normalization of data, and small sample data augmentation are carried out. A homogenization sampling method is proposed to extract training and testing samples. Experimental results show that IACO-BP algorithm has better accuracy and stability in ammunition storage reliability prediction than BP network, PSO-BP, and ACO-BP algorithm.