A premixed air-fuel mixture supply device, combined with a combustor liner included in a combustor, includes a prevaporizing, premixing unit having inner and outer walls defining a prevaporizing, premixing chamber, and a wall surrounding an end part of the outer wall so as to define a secondary combustion air passage together with the end part of the outer wall around the prevaporizing, premixing chamber. A tail part of the outer wall is shaped in an atomization lip. The extremity of the tail part of the atomization lip is formed in a sharp edge or is cut perpendicularly or substantially perpendicularly to the flowing direction of the combustion air.