We consider the question of developing a deep learning algorithm for predicting a patient's blood glucose levels. More precisely, suppose that we are given estimates of a patient's past blood glucose concentrations. Our goal then is to use these past measurements to predict the patient's blood glucose concentration sometime in the future. The highlights of our discussion will include the design of the algorithm and numerical results that demonstrate how deep learning can outperform shallow networks in this application. This is joint work with Hrushikesh Mhaskar and Sergei Pereverzyev.