As a convenient, economical, and eco-friendly travel mode, bike-sharing greatly improved urban mobility. However, it is often very difficult to achieve a balanced utilization of shared bikes due to the asymmetric spatio-temporal user demand distribution and the insufficient numbers of shared bikes, docks, or parking areas. If we can predict the short-run bike-sharing demand, it will help operating agencies rebalance bike-sharing systems in a timely and efficient way. Compared to the statistical methods, deep learning methods can automatically learn the relationship between the inputs and outputs, requiring less assumptions and achieving higher accuracy. This study proposes a Spatial-Temporal Graph Attentional Long Short-Term Memory (STGA-LSTM) neural network framework to predict short-run bike-sharing demand at a station level using multi-source data sets. These data sets include historical bike-sharing trip data, historical weather data, users' personal information, and land-use data. The proposed model can extract spatio-temporal information of bike-sharing systems and predict the short-term bike-sharing rental and return demand. We use a Graph Convolutional Network (GCN) to mine spatial information and adopt a Long Short-Term Memory (LSTM) network to mine temporal information. The attention mechanism is focused on both temporal and spatial dimensions to enhance the ability of learning temporal information in LSTM and spatial information in GCN. Results indicate that the proposed model is the most accurate compared with several baseline models, the attention mechanism can help improve the model performance, and models that include exogenous variables perform better than the models that only consider historical trip data. The proposed short-term prediction model can be used to help bike-sharing users better choose routes and to help operators implement dynamic redistribution strategies.