The invention relates to a scavenging air box assembly of a free piston engine, which comprises a scavenging air box and is characterized in that: the volume of the scavenging air box is equal to thatof a crankcase of the original engine, which aims at ensuring that the compression ratio of the scavenging air box is equal to that of the crankcase of the original engine; the matching position of the scavenging air box and a link rod is provided with a bushing which is an oil bearing; the link rod is connected with the bushing in transition fit, connected with the scavenging air box in shrinkage interference fit and fixed by bolts; the inner surface of the bushing is provided with two pressure-relieving grooves used for exerting sealing effect with a lubricating oil film and a guiding groove used for preventing the link rod from rotating during the moving process; and the guiding groove matches with a key arranged on the link rod. The scavenging air box assembly can overcome the defectsthat the movement of the piston component is difficult to control as the early free piston engine has complicated structure and relatively large mass and volume; the scavenging air box has the dual functions of storing pre-ignition mixed gases and serving as an air cushion, simplifies devices of the system as well as lowers cost simultaneously and increases economic benefit.