The objective of this paper is to design a robust observer-based adaptive controller for an intravenous glucose tolerance test (IVGTT) model of Type 1 Diabetes Mellitus (T1DM) patients. The model is assumed to be nonlinear and uncertain. The robust observer estimates the states of the uncertain T1DM model. Once the states are estimated, an adaptive control technique based on Lyapunov's second method is proposed to achieve the desired closed-loop performance for an uncertain system. The results presented here depict that the design philosophy can avoid severe hypoglycaemia (glucose concentration level below 50 mg/dl), bringing down the glucose concentration to a safe level within a specified time of 120 min. Restoring and maintaining the plasma glucose concentration in T1DM patients in the euglycaemic range (70–180 mg/dl) by appropriate insulin infusion under meal disturbances and parametric variations of are effectively handled with the proposed controller. The realistic situation for the patient model like consideration of (i) only one measurable state, and (ii) uncertain as well as time-varying model parameters addressing inter- and intra-patient variability, respectively, are taken into account. The complexity of the T1DM model leads to a new integrated design methodology, combining robustness and adaptive philosophy for the first time.