Bike-sharing is a new low-carbon and environment-friendly mode of public transport based on the "sharing economy". Since 2017, the bike-sharing market has boomed in China's major cities. Bikes equipped with GPS transmitters are docked along sidewalks that can be easily accessed through smartphone apps. However, this new form of transport has also led to problems, such as illegal parking, vandalism, and theft, each of which presents a major administrative challenge. Further, imbalances in user demand and bike availability need to be overcome to ensure a convenient, flexible service for customers. Hence, predicting a cyclist's destination could be of great importance to shared-bike operators. In this paper, we propose an innovative deep learning model to predict the most probable destination for each user. The model, called destination prediction network based on spatiotemporal data (DPNst), comprises three steps. First, the data is preprocessed and a pool of likely candidate destinations is generated based on frequent item mining. This candidate set is then used to build the DPNst model: a long short-term memory network learns the user's behavior; a convolutional neural network learns the spatial relationships between the origin and the candidate destinations; and a fully connected neural network learns the external features. In the final step, DPNst dynamically aggregates the output of the three neural networks based on the given data and generates the predictions. In a series of experiments on real-world stationless bike-sharing data, DPNst returned an F1 score of 42.71% and demonstrated better performance overall than the compared baselines.