A hybrid system based on a micro gas turbine (µGT) and a high-temperature fuel cell, i.e., molten carbonate fuel cell (MCFC) or solid oxide fuel cell (SOFC), is expected to achieve a much higher efficiency than conventional distributed power generation systems. In this study, a cycle analysis method and the performance evaluation of a µGT-MCFC hybrid system, of which the power output is 30 kW, are investigated to clarify its feasibility. We developed a general design strategy in which a low fuel input to a combustor and higher MCFC operating temperature result in a high power generation efficiency. A high recuperator temperature effectiveness and a moderate steam-carbon ratio are the requirements for obtaining a high material strength in a turbine. In addition, by employing a combustor for complete oxidation of MCFC effluents without additional fuel input, i.e., a catalytic combustor, the power generation efficiency of a µGT-MCFC is achieved at over 60% (LHV).