Biogas is an abundant renewable energy source which can be produced by anaerobic treatment of biological waste such as sewage sludge, agro-industrial waste, and industrial animal waste. The utilization of biogas instead of fossil fuels in a solid oxide fuel cell (SOFC)-based system is a promising choice to achieve a fossil-free and sustainable energy future. A biogas-fed decentralized SOFC combined heat and power (CHP) system model is proposed and analyzed. The system consists of a pre-reformer, an SOFC stack, an afterburner and a heat-recovery boiler. The system model integrates a multi-scale hierarchical three-dimensional SOFC stack model with zero-dimensional balance of power component models, which enables simultaneous investigations of both the overall system performance and the stack-internal distributed properties down to the electrode scale. The effects of steam/carbon ratio, biogas composition and operation voltage of the SOFC stack on the electrical and CHP efficiencies of the system, as well as the temperature gradient within the SOFC stack were studied. The proposed system model is demonstrated as an insightful and powerful tool for designing hybrid SOFC combined heat and power systems.