Predicting short-term urban water demand is essential for water resource management and directly impacts urban water resource planning and supply–demand balance. As numerous factors impact the prediction of short-term urban water demand and present complex nonlinear dynamic characteristics, the current water demand prediction methods mainly focus on the time dimension characteristics of the variables, while ignoring the potential influence of spatial characteristics on the temporal characteristics of the variables. This leads to low prediction accuracy. To address this problem, a short-term urban water demand prediction model which integrates both spatial and temporal characteristics is proposed in this paper. Firstly, anomaly detection and correction are conducted using the Prophet model. Secondly, the maximum information coefficient (MIC) is used to construct an adjacency matrix among variables, which is combined with a graph convolutional neural network (GCN) to extract spatial characteristics among variables, while a multi-head attention mechanism is applied to enhance key features related to water use data, reducing the influence of unnecessary factors. Finally, the prediction of short-term urban water demand is made through a three-layer long short-term memory (LSTM) network. Compared with existing prediction models, the hybrid model proposed in this study reduces the average absolute percentage error by 1.868–2.718%, showing better prediction accuracy and prediction effectiveness. This study can assist cities in rationally allocating water resources and lay a foundation for future research.