Recent decades have witnessed great development of stochastic optimization in training deep neural networks. Learning rate scheduling is one of the most important factors that influence the performance of stochastic optimizers like Adam. Traditional methods seek to find a relatively proper scheduling among a limited number of pre-defined rules and might not accommodate a particular target problem. Instead, we propose a novel Graph-Network-based Scheduler (GNS), aiming at learning a specific scheduling mechanism without restrictions to existing principles. By constructing a directed graph for the underlying neural network of the target problem, GNS encodes current dynamics with a graph message passing network and trains an agent to control the learning rate accordingly via reinforcement learning. The proposed scheduler can capture the intermediate layer information while being able to generalize to problems of varying scales. Besides, an efficient reward collection procedure is leveraged to speed up training. We evaluate our framework on benchmarking datasets, Fashion-MNIST and CIFAR10 for image classification, and GLUE for language understanding. GNS shows consistent improvement over popular baselines when training CNN and Transformer models. Moreover, GNS demonstrates great generalization to different datasets and network structures.