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In recent years, many spatial-temporal graph convolutional network (STGCN) models are proposed to deal with the spatial-temporal network data forecasting problem. These STGCN models have their own advantages, i.e., each of them puts forward many effective operations and achieves good prediction results in the real applications. If users can effectively utilize and combine these excellent operations integrating the advantages of existing models, then they may obtain more effective STGCN models thus create greater value using existing work. However, they fail to do so due to the lack of domain knowledge, and there is lack of automated system to help users to achieve this goal. In this paper, we fill this gap and propose Auto-STGCN algorithm, which makes use of existing models to automatically explore high-performance STGCN model for specific scenarios. Specifically, we design Unified-STGCN framework, which summarizes the operations of existing architectures, and use parameters to control the usage and characteristic attributes of each operation, so as to realize the parameterized representation of the STGCN architecture and the reorganization and fusion of advantages. Then, we present Auto-STGCN, an optimization method based on reinforcement learning, to quickly search the parameter search space provided by Unified-STGCN, and generate optimal STGCN models automatically. Extensive experiments on real-world benchmark datasets show that our Auto-STGCN can find STGCN models superior to existing STGCN models with heuristic parameters, which demonstrates the effectiveness of our proposed method.