In 2015 the United Nations proposed the Sustainable Development Goals (SDGs), a set of universal goals for meeting the urgent environmental, political and economic challenges in the world. Universities play an important role to support and contribute to the SDGs mainly through education and research. To evaluate the contributions through research, universities aim at relating their scientific publications to SDGs, and automatically quantify the connectedness of these publications to the detailed targets and the unique indicators under SDGs. In this paper, we apply deep learning techniques to estimate the unknown indicators (third level) and targets (second level) for each publication, and output all its possible goals (first level). Specifically, we first exploit the dependency of categories at different levels (goals, targets, and indicators) to extract the dependent label features. Then we calculate the degree of matching between categories and publications in a bottom-up way and design a hierarchical structure to transfer such matching information level by level until obtaining the predicted SDGs of the publications. This is the first application of a deep learning method on this SDG prediction task and our experiments clearly demonstrate the good performance of our model on this real-world SDGs matching task, the extraction of key information as well as the prediction of potential sub-categories. As auxiliary analysis, we visualize the extraction of key semantic information and the probability of the hierarchical SDG categories.