A solid oxide fuel cell (SOFC)-gas turbine (GT) hybrid system combined with anode and combustor recirculation is investigated in this paper. The ejector technology is introduced to perform the recirculation loops, the hybrid system mainly consists of a SOFC stack, a micro gas turbine, a catalytic combustor, a combustor recirculation loop which is used to raise the electrical efficiency and output power of SOFC, and an anode recirculation loop to improve the hydrogen yield and reduce the risk of carbon deposition. This paper uses the detailed mathematical models of the SOFC-GT hybrid system to study the effect of anode and combustor recirculation on its performances. Results show that the maximum output power and electrical efficiency of SOFC-GT are 183kW and 61.8% respectively when the recirculation ratio of anode and combustor exhaust varied from 0 to 0.4. And the maximum electrical efficiency is reached under the recirculation ratio of anode and combustor are 0.4 and 0.4 respectively, which is increased by almost 3.67% compared with the system without recirculation loop.