In this paper, we consider the problem of blood glucose control for type 1 diabetic patients. In particular, we focus on developing control algorithms for an Artificial Pancreas which is a portable or implantable automated insulin delivery system composed of a continuous glucose monitor, an insulin pump, and a control law that links the measured blood glucose concentration and insulin delivery. We have designed Receding Horizon Control (RHC) (which is also known as the Model Predictive Control) for two specific patients, respectively, based on a data-driven linear time-varying state-space model developed in for each patient using clinical data. The control parameters are tuned specifically for each patient. For patient 1, the RHC algorithm performs well with no information (e.g., amount and time) of meal intake, which results in the so-called feedback alone control. For patient 2, information of meal intake is necessary for the RHC algorithm to reach acceptable closed-loop performance, which results in the so-called feedback plus feedforward control. For both patients, we evaluate the performance of the RHC designs via simulation and compare the simulation results with clinical data. We also test the robustness of the RHC design with respect to estimation errors in the amount of carbohydrate content (CHO) of the meal.