This communication presents the thermodynamic analysis along with a detailed parametric study of an irreversible regenerative MHD power cycle. The power output is adopted as the objective function and optimized with respect to the cycle temperature ratio for a typical set of operating parameters. The power output is found to be an increasing function of the effectiveness and the heat capacitance rates on the hot- and cold-side reservoirs, the regenerative effectiveness, and the compressor and generator efficiencies, while it is found to be a decreasing function of the working fluid heat capacitance rates and the Mach number. The effects of the cold-side effectiveness and heat capacitance rate are found to be more than those of the other side effectiveness and heat capacitance rates on the performance of the cycle. The effect of the compressor efficiency is found to be more than that of the generator efficiency on the power output while it is reverse in the case of thermal efficiency. It is also found that there is an optimum relation among the various heat capacitance rates at which the cycle attains the maximum performance.