Electron gun is an important part of vacuum electronic devices, and the foil-less diode is one kind of the vacuum electron guns. In this paper, a miniature vacuum electron gun which is used in terahertz backward wave oscillator is studied both by theoretical analysis and numerical simulation, especially the production mechanism of annular electron beam and the propagation characteristics of the beam. First, the performance of foil-less diode was qualitatively described through the theoretical analysis. Second, the static electric field in the diode was calculated by numerical simulation. Third, the device performances were optimized by using 2.5D particle-in-cell simulation software. Finally, a set of optimal operating parameters were achieved.