An efficient adaptive mesh method is prestmted for constituting automatically the numercal grids to adapt the severe change of space scales of ignition and reactive flow problems. By combining this technique with ALE numerical method, a set of partial differential equations that control droplet ignition and combustion process is solved. The results obtained turn out clearly the space time distributions of physical parameters of gas phase around the droplet and show the calculation efficiency is greatly improved while without a loss of accuracy.