This work presents a Phenomenological-Based Semi-physical Model (PBSM) for the role of the pancreas in the glucose homeostasis. The model focuses on flow and concentration changes of insulin and glucagon that leaving the pancreas towards the portal vein, according to the levels of glucose detected by the pancreas in the bloodstream. Unlike other mathematical models, the PBSM obtained has a greater structural and parametric interpretability. The results obtained show a good agreement with respect to one sets of experimental data, in which adjustment factors are included to compensate the absence of paracrine effects in the model.