This paper presents a model-based design optimization strategy for ground source heat pump systems with integrated solar photovoltaic thermal collectors (GSHP-PVT). A dimension reduction strategy using Morris global sensitivity analysis was first used to determine the key design parameters of the GSHP-PVT system. A model-based design optimization strategy was then formulated to identify the optimal values of the key design parameters to minimize the life-cycle cost (LCC) of the GSHP-PVT system, in which an artificial neural network (ANN) model was used for performance prediction and a genetic algorithm (GA) was implemented as the optimization technique. A simulation system of a GSHP-PVT system developed using TRNSYS was used to generate necessary performance data for dimension reduction analysis, and for the ANN model training and validation. The results showed that the ANN model used was able to provide an acceptable prediction of the operational cost of the GSHP-PVT system. In comparison to two baseline cases, the 20-year life cycle cost (LCC) of the GSHP-PVT system studied can be decreased by 20.1% and 10.2% respectively, when using the optimal values determined by the proposed optimization strategy. This design optimization strategy can be potentially adapted to formulate the design optimization strategies for GSHP systems and other building energy systems.