The invention discloses a micro-combustor for metal mesh heat storage and flame stabilization and a combustion method thereof. The micro-combustor for the metal mesh heat storage and flame stabilization comprises a combustor outer barrel and an igniter arranged in the combustor outer barrel; a combustor comprises a hollow blunt body, a multi-hole medium disc and a metal mesh, wherein the longitudinal section of the hollow blunt body is in the shape of an inverted triangle, the multi-hole medium disc is arranged on the hollow blunt body, the metal mesh is arranged on the multi-hole medium disc, and the bottom of the hollow blunt body is connected with a fuel channel. By means of the multi-hole medium disc, it is guaranteed that fuel is dispersed evenly, the superficial area of the fuel is increased, and the evaporation rate is sped up. A high temperature low-velocity backflow zone is formed near an outlet of the hollow blunt body, the dwell time of the fuel is increased, the metal mesh is taken as a heat storage medium and has the functions of absorbing heat and releasing heat, and the flame temperature can be maintained at a certain level; compared with other combustors, by means of the micro-combustor for the metal mesh heat storage and flame stabilization, a flame can be made to be attached to the metal mesh stably, sharply swing or up and down fluctuation of the flame does not occur along with changes of working conditions, and the stability of combustion of liquid hydrocarbon under micro scale is greatly promoted.