There is a significant push to develop closed-loop control systems to deliver insulin for type 1 diabetic subjects. As part of this process, mathematical models are required to test and validate the proposed algorithms. There are several published physiology-based models of glucose and insulin dynamics in the literature, however, all of them were derived using data from subjects without diabetes. For this particular study we have selected one of the recently published models, by Hovorka et al., replacing the subcutaneous insulin infusion model with the one described by Wilinska et al., Five subjects with type 1 diabetes underwent a hyperinsulinemic-euglycemic clamp with a meal challenge and corresponding subcutaneous insulin bolus. The data collected were used to fit the model parameters using global optimization methods. Our results show that the model is capable of describing the observed dynamics for type 1 subjects under the experimental conditions, and as such can be used to simulate subject behavior under the experimental conditions.