Sheet-beam formation has been studied using the combination method of theory analysis and simulation verification. A design theory of the sheet-beam electron gun has been proposed. The beam voltage, the beam current, the half-thickness of beam at the waist position, the half-thickness of the cathode, and the width of the cathode are used to calculate the parameters of the sheet-beam electron gun such as the cathode cylindrical radius, the anode-cathode spacing, the anode cylindrical radius, and the throw. Then through simulation, the sheet-beam electron gun for millimeter-wave vacuum electron devices are set up based on the theoretical results.