For people with type 1 diabetes, good blood glucose control is essential to keeping serious disease complications at bay. This entails carefully monitoring blood glucose levels and taking corrective steps whenever they are too high or too low. If blood glucose levels could be accurately predicted, patients could take proactive steps to prevent blood glucose excursions from occurring. However, accurate predictions require complex physiological models of blood glucose behavior. Factors such as insulin boluses, carbohydrate intake, and exercise influence blood glucose in ways that are difficult to capture through manually engineered equations. In this paper, we describe a recursive neural network (RNN) approach that uses long short-term memory (LSTM) units to learn a physiological model of blood glucose. When trained on raw data from real patients, the LSTM networks (LSTMs) obtain results that are competitive with a previous state-of-the-art model based on manually engineered physiological equations. The RNN approach can incorporate arbitrary physiological parameters without the need for sophisticated manual engineering, thus holding the promise of further improvements in prediction accuracy.