In a generating method and a generator of mist or fine-bubble, with a simple and small configuration, application into a wide range kind of liquid is enabled, and generating stably the mist or the fine-bubbles or both is enabled. The generator is provided with a piezoelectric substrate which equips two or more comb-like electrodes on a surface and arranged so that the surface may intersect the mutual interface of the gas and the liquid and a part of piezoelectric substrate is put in a liquid, and a surface acoustic wave excited on the surface with the electrode is made to propagate along the surface so that may exist in the upper and lower sides of an interface. The surface acoustic wave generates mist in the gas side which is above the interface, and generates fine-bubbles in the liquid side which is below the interface. Since the mist and the fine-bubbles are generated with the surface acoustic wave, without being based on mechanical operation for generating a turning stream, the mist and the fine-bubbles can be stably generated in the simple and small configuration.