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The demand for clean energy continues to increase as the human society becomes more aware of environmental challenges such as global warming. Various power systems based on high-temperature fuel cells have been proposed, especially hybrid systems combining a fuel cell with a gas turbine (GT), and research on carbon capture and storage (CCS) technology to prevent the emission of greenhouse gases is already underway. This study suggests a new method to innovatively enhance the efficiency of a molten carbonate fuel cell (MCFC)/micro GT hybrid system including carbon capture. The key technology adopted to improve the net cycle efficiency is off-gas recirculation. The hybrid system incorporating oxy-combustion capture was devised, and its performance was compared with that of a post-combustion system based on a hybrid system. A MCFC system based on a commercial unit was modeled. Externally supplied water for reforming was not needed as a result of the presence of the water vapor in the recirculated anode off-gas. The analyses confirmed that the thermal efficiencies of all the systems (MCFC stand-alone, hybrid, hybrid with oxy-combustion capture, hybrid with post-combustion capture) were significantly improved by introducing the off-gas recirculation. In particular, the largest efficiency improvement was observed for the oxy-combustion hybrid system. Its efficiency is over 57% and is even higher than that of the post-combustion hybrid system.