The blood glucose metabolism of a diabetic is a complex nonlinear process closely linked to a number of internal factors which are not easily accessible to measurements. Based on accessible information ?such as continuous glucose monitoring (CGM) measurements and information on the amount of ingested carbohydrates and of delivered insulin? the system appears highly stochastic and the quantity of main interest, the blood glucose concentration, is very difficult to model and to predict. In this paper, we approximate the glucoseinsulin system by a linear model with physiological transformed input signals. Considering the time varying characteristics of this system, a normalized least mean squares (NLMS) algorithm with an optimized variable gain is utilized for the recursive estimation of the model coefficients, and its resulting mean square error (MSE) convergence property is investigated. Our experimental results (15 Type 1 diabetic patients) were analyzed from a modeling theory, and also from a clinical point of view using Continuous Glucose-Error Grid Analysis (CG-EGA).