RF breakdown and mode competition are the main causes of power reduction and pulse shortening of klystron oscillator (RKO). This paper introduces an extended interaction extraction structure, which can effectively reduce the RF electric field of the extraction cavity and increasing the power capacity. The traditional double-gap extraction structure converts electron energy into microwave energy in an extraction cavity and shares one channel for output. However, the extended interaction extraction structure adopts a distributed extraction cavity instead of a centralized extraction cavity, which increases the output channel, thus it can effectively improve the beam-wave conversion efficiency and reduce the RF electric field of the extraction cavity. The results of particle simulation show that the output power is 2.14 GW, 2.22 GW, 2.35 GW for the traditional two-gap extraction cavity, the two-gap extraction cavity and the three-gap extended-interaction extraction cavity, respectively, when the diode voltage is 561 kV and the magnetic field strength is 0.5 T. The maximum RF electric field of the extraction cavity is 1.50 MV/cm, 1.21 MV/cm and 1.10 MV/cm, respectively. The beam-wave conversion efficiency was 35.7%, 36.9% and 39.1%, respectively. The operating frequency of the device is 12.52 GHz. In the 3D simulation, by changing the S parameter of the cathode structure and designing a new reflector, the mode competition caused by TM₁₁₃ mode of the modulation cavity is effectively suppressed, which laid the foundation for subsequent experiments.