A W-band dual-mode Extended Interaction Oscillator(EIO) is designed in this paper, achieving a dual 2π mode through the coupling between the 2π mode and a specific cavity mode. By adjusting the cavity's structural parameters, the frequency separation of the dual 2π modes is controlled, and the variations in high-frequency parameters during this process are analyzed. Particle-In-Cell(PIC) simulations demonstrate that, with a 3.2 mm×0.2 mm, 2 A sheet electron beam, the lower-frequency 2π mode operates at 91.01 GHz with an output power of 7.29 kW and an electron efficiency of 17.45% at an electron beam voltage of 20.90 kV. The higher-frequency 2π mode achieves 91.18 GHz, 4.76 kW output power, and 11.26% efficiency at 21.15 kV. The results verify that the dual 2π mode EIO possesses the capability for high-power, high-efficiency output while providing theoretical support for the realization of dual 2π modes.