Insulin secretion from pancreatic β-cells in response to sudden glucose stimulation is biphasic. Prolonged secretion in vivo requires synthesis, delivery to the plasma membrane (PM) and exocytosis of insulin secretory granules (SGs). Here, we provide the first agent-based space-resolved model for SG dynamics in pancreatic β-cells. Using recent experimental data, we consider a single β-cell with identical SGs moving on a phenomenologically represented cytoskeleton network. A single exocytotic machinery mediates SG exocytosis on the PM. This novel model reproduces the measured spatial organization of SGs and insulin secretion patterns under different stimulation protocols. It proposes that the insulin potentiation effect and the rising second-phase secretion are mainly due to the increasing number of docking sites on the PM. Furthermore, it shows that 6 min after glucose stimulation, the 'newcomer' SGs are recruited from a region within less than 600 nm from the PM.