A circuit design of sheet-beam extended interaction oscillator (SB-EIO) with an overmoded staggered grating array is embodied in theoretical analyses which combined with particle-in-cell (PIC) simulation. Mode and dispersion analyses on the design of the TM41-2π mode EIO demonstrated that the optimized cutoff frequency and the dimensions of the SWS noticeably suppress non-operating lower order modes. The overmoded structure only allowed the desired 4th order mode to propagate in the structure. In addition, this structure benefit from a mm-level transverse size structure, so that it can be a potential solution for the applications (such as communications and spectroscopy) lack in output power. The newly designed EIO is simulated with copper used as the background material, and the ∼0.375 THz radiation power of ∼105W is achieved when an electron beam with 1.3 A and 44.5 kV is injected. The designed circuit structure can be widely applied to sheet beam devices for THz RF generation.