A method of and an apparatus for expanding the mode field diameter of an optical fiber by heating a specified region of the optical fiber with a uniform or desired temperature distribution for forming a thermally-diffused expanded core (TEC). The mode field diameter of the optical fiber is expanded by heating an optical fiber 1 with a burner 11 so as to thermally diffuse the dopant forming the refractive-index profile. The burner 11 has a heating surface 11a in which a plurality of gas-issuing holes 12 are arranged such that a plurality of parallel rows each of which is composed of a plurality of gas-issuing holes 12 are parallel to the axis of the optical fiber 1.