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Shared bicycles provide a green, environmentally friendly, and healthy mode of transportation that effectively addresses the “final mile” problem in urban travel. However, the uneven distribution of bicycles and the imbalance of user demand can significantly impact user experience and bicycle usage efficiency, which makes it necessary to predict bicycle demand. In this paper, we propose a novel shared-bicycle demand prediction method based on station clustering. First, to address the challenge of capturing patterns in station-level bicycle demand, which exhibits significant fluctuations, we employ a clustering method that combines graph information from the bicycle transfer graph and potential energy. This method aggregates closely related stations into corresponding prediction regions. Second, we use the GCN-CRU-AM (Graph Convolutional Network-Gated Recurrent Unit-Attention Mechanism) model to predict bicycle demand in each region. This model extracts the spatial information and correlation between regions, integrates time feature data and local weather data, and assigns weights to the input features. Finally, experimental results based on the data from Citi Bike System in New York City demonstrate that the proposed model achieves a more accurate demand prediction.