This paper describes an application of finite-time thermodynamics to optimize the power output of endoreversible intercooled Brayton cycles coupled to two heat reservoirs with infinite thermal capacitance rates. The effects of intercooling on the maximum power and maximum-power efficiency of an endoreversible Brayton cycle are examined. With appropriate temperature ratios of turbines and compressors being used, the maximum power output of an endoreversible intercooled Brayton cycle can be higher than that of an endoreversible simple Brayton cycle without lowering the thermal efficiency. New diagrams for maximum power, maximum-power thermal efficiency, and optimum temperature ratios of turbines and compressors are reported.