Micro-pulse electron gun (MPG) employs the basic concept of multipacting to produce high-current and short-pulse electron beams from a radio-frequency (RF) cavity. The concept of MPG has been proposed for more than two decades. However, the unstable operating state of MPG vastly obstructs its practical applications. This paper presents a study on the steady operating state of a micro-pulse electron gun with theory and experiments. The requirements for the steady operating state are proposed through the analysis of the interaction between the RF cavity and the beam load. Accordingly, a MPG cavity with the frequency of 2856 MHz has been designed, constructed, and tested. Some primary experiments have been finished. Both the unstable and stable operating states of the MPG have been observed. The stable output beam current has been detected at about 3.8 mA. Further experimental study is under way now.