In this paper, the power density, defined as the ratio of power output to maximum specific volume in the cycle, is taken as the objective for performance analysis of an endoreversible closed Brayton cycle coupled to variable temperature heat reservoirs in the viewpoint of finite time thermodynamics or entropy generation minimization. The analytical formulae about the relations between power density and pressure ratio are derived with heat resistance losses in the hot and cold side heat exchangers. The obtained results are compared with those results obtained by using the maximum power criterion. The influences of some design parameters on the maximum power density are provided by numerical examples, and the advantages and disadvantages of maximum power density design are analyzed. The power plant design with maximum power density leads to a higher efficiency and smaller size. When the heat transfer is effected ideally and the thermal capacity rates of the two heat reservoirs are infinite, the results of this paper become those obtained in recent literature.