Combined cooling, heating and power (CCHP) system with the prime mover set of solid oxide fuel cell-gas turbine (SOFC-GT) would feature with high electrical efficiency, but contain the highly coupled equipment units for cooling, heating and electricity supplies. Due to such complex nature of multiple supplies and demands, the previously developed control strategies were not suitable, and it is a challenge to develop an appropriate control strategy for the SOFC-GT CCHP system. Therefore, a new approach, called multi-supply-multi-demand (MSMD) control strategy, is proposed in this paper. The MSMD control includes two core algorithms: rolling optimization (RO) and feedback correction (FC). RO is used to determine the operation of energy supply equipment units based on the forecasting weather and loading information of the next 24 h. FC is applied for continual mitigation in case any difference between the actual and predicted energy demands. In the SOFC-GT CCHP system with energy storages for building application, the effectiveness of the MSMD control strategy was tested. It was found that RO could determine the operating schedules of the related equipment units at lower primary energy consumption than the conventional mean, while FC could effectively rectify the prediction errors incurred from the real-time loading conditions.