This paper presents the work on a simple, natural gas-fed, hybrid solid oxide fuel cell-gas turbine (SOFC-GT) power-generation system. The system consists of an internal-reforming SOFC (IRSOFC) stack, a combustor, a GT, two compressors and three recuperators. Two case studies are conducted with particular attention on the effects of operating pressure and fuel flow-rate on the performance of the components and overall system. Results show that an internal-reforming hybrid SOFC-GT system can achieve an electrical efficiency of more than 60% and a system efficiency (including waste heat recovery for co-generation) of more than 80%. It is also found that increasing the operating pressure will improve the system efficiency, whereas increasing the fuel flow-rate (while keeping the fuel utilisation rate unchanged) causes the system efficiency to decrease. In the latter case, the increase in system fuel consumption is relatively higher which removes the benefit of increase in SOFC stack and turbine power output.