The power output of a simple finite-time Brayton closed cycle for an indirect gas-cooled nuclear power plant is analyzed. The system adopted is a reversible Brayton cycle coupled to a reactor (heat source) and a cooling fluid (heat sink) by heat transfer. Mathematical expression is derived for the power output of the nuclear power plant, and the maximum power output is found. The maximum bound provides a basis for designing a real indirect gas nuclear power plant and for a performance comparison with existing power plants.