A multi-stage Stirling cycle machine and a steady-state operating parameter control method therefor are disclosed. In the Stirling cycle machine, a mechanical energy input piston, a mechanical energy transfer double-acting free piston, and a mechanical energy output piston constitute a plurality of Stirling working units which are arranged in stages. The mechanical energy input piston is connected to a mechanical energy input apparatus. The mechanical energy output piston is connected to a mechanical energy output apparatus. When the Stirling cycle machine is used as an engine, a relatively small amount of mechanical energy is input into a mechanical energy input piston in a set of pistons, the mechanical energy is amplified by a multi-stage Stirling unit, and a relatively large amount of mechanical energy is then output by a mechanical energy output piston.