The invention discloses a peripherally-actuated auxiliary moment generator for an under-actuated system and belongs to electromagnetic moment type moment generators. The peripherally-actuated auxiliary moment generator for the under-actuated system is characterized by comprising a shell, a magnet set, an armature winding, a front end cover, a rear end cover, a motor, a motor support and a load, wherein the shell is in matched connection with the under-actuated system through a gear, a cam or an impeller. By the aid of the electromagnetic induction principle, the motor is used for actuating the armature winding to rotate in the magnetic field so as to generate the electromagnetic torque opposite to the motor actuating direction, and the magnet set is subjected to the reactive electromagnetic torque opposite to and as equal as the electromagnetic torque of the armature winding so as to provide required moment for the under-actuated system. Particularly, the moment provided by the device is in direct proportion to the velocity, so that control difficulty is remarkably reduced. The peripherally-actuated auxiliary moment generator for the under-actuated system is simple and reliable in design and clear in structure, can be applied to attitude adjustment of one-wheeled robots, satellites, space shuttles and missiles and can also be applied to the fields of overcoming of reactive torque of helicopters or butterfly air vehicles.