The thermodynamic performance analysis of a magnetohydrodynamic (MHD) power plant is performed in this paper. The analytical expressions for the power output and the efficiency are derived for the MHD plant coupled to variable temperature heat reservoirs at constant gas velocity and constant Mach number conditions. In the analysis, the irreversibilities include the irreversible heat transfer losses in the hot and cold side heat exchangers, the irreversible compression loss in the compressor, the irreversible expansion loss in the MHD generator and the effect of finite thermal capacitance rate heat reservoirs. Detailed numerical examples are given.