A single-piston single-unit hydraulic free-piston engine comprises a single-unit fuel pot, a fuel controlling electromagnetic valve, a catalyze bed, a single-piston hydraulic free-piston engine and an electric-control unit. The invention uses high-density hydrogen dioxide or the mixture of hydrogen dioxide and diesel as fuel, and decomposes the fuel via catalysis and decomposition into high-temperature high-pressure mixture gas to drive the single-piston single-unit hydraulic free-piston engine, to exchange the chemical energy of fuel with the hydraulic energy. The invention has high reliability, small volume, low weight and high energy density, or the like, while it can output power in large range by changing the size of engine or the work-frequency of engine. The invention can be used to supply hydraulic energy in non-oxygen condition or oxygen-lack condition.