PURPOSE: A transformer with a damping coil is provided to prevent saturation of a core and reduction of a limited impedance by attaching a damping coil to an air gap leg. CONSTITUTION: An air gap(A) is formed on a core(1). The first and the second wires(3,2) are wound around a leg(1A) of one side of the core(1). The first wire(3) is wound around an inside of the leg(1A). The second wire(2) is wound around an outside of the leg(1A). A main closed magnetic path(4) and a closed magnetic path(5) formed with air gap(A) are connected parallel to the first wire(3). A damping coil(6) is installed at a leg(1B) having the air gap(A).