To provide a multifuel gas turbine combustor capable of combusting gases containing hydrogen in a high concentration with a low NOx while maintaining a low emission performance brought about by the pre-mixture combustion in the main burner, the gas turbine combustor includes a main burner (12) for supplying to and combusting a premixed gas (M), containing a first fuel (F1), within a first combustion region (S1) of a combustion chamber (10), and a supplemental burner (20) for supplying to and combusting a second fuel (F2) of a composition different from that of the first fuel (F1) within a second combustion region (S2) defined downstream of the first combustion region (S1) within the combustion chamber (10). The first fuel (F1) is of a hydrocarbon system and the second fuel (F2) is a gas containing hydrogen in a concentration exceeding the stable combustion limiting concentration of the hydrogen.