This paper presents a model-based optimal control strategy for ground source heat pump systems with integrated solar photovoltaic thermal collectors (GSHP-PVT). The control strategy was formulated using simplified adaptive models and a genetic algorithm (GA) to identify energy efficient control settings for GSHP-PVT systems. The simplified adaptive models were used to predict the system energy performance under various working conditions and control settings, and the model parameters were continuously updated using the recursive least squares (RLS) estimation technique with exponential forgetting. The performances of the adaptive models and the control strategy were evaluated based on a virtual simulation system representing a GSHP-PVT system for residential applications. The performance of the major adaptive models was also validated using the experimental data. The results showed that the simplified adaptive models used were able to provide acceptable energy performance prediction. The optimal control strategy can save energy consumption by 7.8%, 7.1% and 7.5%, and increase electricity generation by 4.4%, 6.2% and 5.1%, during the whole cooling, heating and transition periods considered, respectively, in comparison to a conventional control strategy. The findings obtained from this study could be potentially used to drive the development of advanced control strategies suitable for real-time applications.