The main content of this paper is the design and simulation of a multiple sheet beam extended interaction oscillator (EIO) based on pseudospark-sourced (PS) electron beams. EIOs, which operate in high frequency waveband, have a huge demand for high current density. The PS electron beam is featured with high current density and no need of the external focusing magnetic field. At the same time, EIO's multiple sheet beams are crucial to its efficiency improvement. In this paper, the authors propose the extended interaction circuit containing a coaxial structure operating in the $T M_{31}$ mode, which results in an efficient beam-wave interaction due to electron beams' large cross-section area. The EIO with six sheet beams operates at a voltage of 41.5 kV with a total current of almost $8 \mathrm{~A}$ (equally distributed among the six beams). The simulation results showed that the power obtained from the output is $21.2 \mathrm{~kW}$ at 144.8 GHz, and that the corresponding efficiency is about 6.4 %, taking into account the conductivity of $3 \times 10^7 \mathrm{~S} / \mathrm{m}$.