To understand the complex continuous microwave drying of germinated brown rice (GBR) and clarify the drying characteristics, the heat and mass transfer of GBR under continuous microwave drying was investigated numerically and experimentally. A three-dimensional model of coupled multi-physics fields involving the transmission of microwave field, heat transfer and mass (moisture) transfer was developed to characterise the drying process of GBR in a continuous microwave dryer. The implementation strategy based on discrete-combined approach was proposed to achieve the simulation of continuous microwave drying of moving materials with the mutual cooperation of the computer simulation software and independently developed program code. For the continuous microwave drying of GBR, the relatively uniform distribution of electric field strength applied to the grain layer depended on the reasonable arrangement pattern of magnetrons and suitable microwave power output. The movement of materials can effectively reduce excessive absorption of microwave energy by the grain layer, and achieve uniform distribution of temperature and moisture content and high drying uniformity assisted by the synergistic effects of microwave heating, moisture evaporation and ventilation convection. The developed model and simulation strategy may provide guidance for understanding and analysis of continuous microwave drying process of granular materials such as GBR.