In this paper, we present a mathematical model of diabetes mellitus, which is a metabolic disease concerned with the regulation process of glucose in the body by the pancreatic insulin. This paper considers the disappearance of glucose due to insulin action (insulin-dependent) as well as the disappearance of glucose due to tissue uptake such as the brain and nerve cells (insulin-independent) and rise in glucose level due to infusion through meal intake, oral glucose intake, continuous nutrition absorption and constant infusion. The linear and non-linear cases are considered and the model is analyzed using Lyapunov’s method. Conditions for local as well as global stability are obtained. Numerical simulations are carried out and graphs are also generated to indicate the role of insulin in the regulation process of glucose in the human body.