In the present study, a recuperator is suggested to improve the thermal efficiency of a micro gas turbine. Primary design parameters of the recuperator are determined from the ideal cycle analysis. The counter flow plate-fin heat exchanger with offset strip fins is chosen as the type of the recuperator. In order to satisfy the design constraints which are the minimum effectiveness and the maximum pressure drop, the optimization for the internal structure of the recuperator is performed with varying the fin spacing and the fin height of offset strip fins. Also the effects of the thermal conductivity of fins and separation plates and the longitudinal heat conduction on the thermal performance of the recuperator are investigated.