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Pseudospark-sourced electron beam is a promising candidate for driving vacuum electronic devices to generate mil-limeter wave and terahertz wave radiation as it has a very high combined beam current density. However, the inherent velocity spread of the beam, which is difficult to measure in experiment, has a great influence on the operating frequency and efficiency of the vacuum electronic device. In this paper, the velocity distribution characteristics of the electron beam produced by a single-gap hollow cathode electron gun are numerically studied and a three-dimensional kinetic plasma simulation model of a single-gap hollow cathode electron gun is built by using particle in cell and Monte Carlo collision methods in Vorpal. Based on the simulation model, the time-dependent evolution of the plasma formation inside the hollow cathode and electron beam generation process are observed. It is demonstrated that the pseudospark-sourced electron beam has a relatively large velocity spread. The time-dependent velocity distribution of the beam is analyzed, and the depen-dence of the beam velocity distribution under various operating conditions such as anode–cathode potential difference, gas pressure, and cathode aperture size are also studied.