To provide a thick and thin fuel combustion burner reinforcing flame stability, and capable of carrying out NOx reduction, load/TDR enhancement, and prevention of vibration combustion and low frequency combustion noise.

The thick and thin fuel combustion burner is composed such that an auxiliary flame hole 13 is provided as a passage outlet for a boundary area supplying premixed gas or air to a boundary between a thin flame hole 11 and a thick flame hole 12, a boundary between the thin flame hole 11 and the auxiliary flame hole 13 or between the thick flame hole 12 and the auxiliary flame hole 13 is formed of a plate member with a rim thickness t of 1 mm or less, and the auxiliary flame hole 13 has a passage width H1 of 0.4-2.0 mm. By such a composition, an eddy is hardly formed above a rim, and by providing the auxiliary flame hole with the passage width of 0.4-2 mm, a flat flame can be formed on an auxiliary flame hole upper part. By the flat flame, stability of both flames of the thick flame and the thin flame can be reinforced.