Because of the larger surface-area-to-volume ratio, micro-discharges can be sustained by surface emission processes. If the cathode is heated, micro-discharge can be sustained mainly by thermionic emission. However, we still knew little about how this kind of plasma is ignited and sustained. In order to explore the breakdown process of dc-driven micro-discharge sustained by thermionic emission, a one-dimensional implicit particle-in-cell/Monte Carlo collision method is adopted, coupled with the external circuit and thermionic emission model. The breakdown process of micro-discharge lasts about 8μs, and this process can be roughly divided into two phases, i.e., pre-breakdown and breakdown phase. The dynamic plasma parameters during the evolution process are analyzed, such as particle density, electron energy distribution function, electric potential, average particle temperature, and particle current density. The plasma electrical characteristics as well as the article and power balance, are also presented to show the evolutionary features of the whole gas breakdown process.