Real-world systems, such as manufacturing or computer systems, can be modeled as multistate network (MSN) consisting of arcs with stochastic capacity. Network reliability for an MSN is described as the probability that the system can meet the demand. The network reliability for demand level d can be computed in terms of the minimal path (calledd-MP). However, efficiently calculating network reliability is challenging in large-scale networks. Deep learning approaches are rapidly advancing several areas of technology, with significant applications in image recognition, parameter adjustment, and autonomous driving. Hence, in this study, we adopt a deep neural network (DNN) model to predict network reliability for a given demand level. To train the DNN model, network information is first used as input data. Then, a DNN model is constructed, including the determination of related functions. Furthermore, Bayesian optimization (BO) is applied to determine related hyperparameters. A practical implementation using a bridge network demonstrates the feasibility of the DNN model. Finally, experiments involving two networks with more nodes and arcs indicate the computational efficiency of combining deep learning methods and the existing d-MP algorithm.