A new radial klystron oscillator driven by intense relativistic electron beam is studied in this paper. A radial intense relativistic electron beam goes through foldaway coaxial cavity , and sel-excites the cavity. The space charge limited current of the radial gap with moderate RF voltage is investigated theoretically and simulatedly. In the radial modulating gap, electron bunches may be generated instantaneously when the radial current is close to or exceeds the limiting current. The new radial klystron oscillator driven by intense relativistic electron beam with foldaway coaxial cavity is designed and simulated by Magic PIC. An output power of 6 GW is generated with 500 kV voltage, 30 kA beam current and the frequency is 1.3 GHz.