Hyperglycaemia in critically ill patients increases the risk of further complications and mortality. A long-term verification of a model that captures the essential glucose- and insulin-kinetics is presented, using retrospective data gathered in an Intensive Care Unit (ICU). The model uses only two patient specific parameters, for glucose clearance and insulin sensitivity. The optimization of these parameters is accomplished through a novel integration-based fitting approach, and a piecewise linearization of the parameters. This approach reduces the non-linear, non-convex optimization problem to a simple linear equation system. The method was tested on long-term blood glucose recordings from 17 ICU-patients, resulting in an average error of 7%, which is in the range of the sensor error. One-hour predictions of blood glucose data proved acceptable with an error range between 7- 11%. These results verify the model’s ability to capture longterm observed glucose-insulin dynamics in hyperglycaemic ICU patients.