Real-world systems, such as transportation system, can be modeled as the stochastic flow networks (SFN) composed of arcs with stochastic capacity. Network reliability of the SFN is described as the probability that system can meet the demand. The network reliability for demand level d can be computed in terms of minimal path (called d-MP for short). However, efficiently calculating the network reliability is a challenge in large-scale networks. Deep learning approaches are rapidly advancing many complicated areas of technology with significant effect in image recognition, parameter adjustment and autonomous driving. Hence, this research is a pilot study to adopt the deep neural networks (DNN) model to predict the network reliability under demand level. To train the DNN model, the network information is first considered as input data. Then, the DNN model is constructed, included the determination of related functions. A practical implement with bridge network further shows the feasibility of the DNN model. Finally, the experimental results for two networks with more nodes and arcs are presented to show the computational efficiency between the deep learning methods and existing d-MP algorithm.