Predictive analytics in higher education has become increasingly popular in recent years with the growing availability of educational big data. Particularly, a wealth of student activity data is available from learning management systems (LMSs) in most academic institutions. However, previous investigations into predictive analytics in higher education using LMS activity data did not adequately accommodate student behaviours in the form of time series. In this study, we have applied a deep learning approach--long short-term memory (LSTM) networks--to analyze student online temporal behaviours using their LMS data for the early prediction of course performance. To reveal the potential of the deep learning approach in predictive analytics, we compared LSTM networks with eight conventional machine-learning classifiers in terms of the prediction performance as measured by the area under the ROC (receiver operating characteristic) curve (AUC) scores. Results indicate that using the deep learning approach, time series information about click frequencies successfully provided early detection of at-risk students with moderate prediction accuracy. In addition, the deep learning approach showed higher prediction performance and stronger generalizability than the machine learning classifiers.