A turbine burner (1) comprising a secondary feed unit for the supply of a backup mixture and a primary feed unit intended for the supply of a primary mixture comprising lean gas, comprising a primary mixture channel (24). The primary mixture channel (24) has an annular wall (28) having a truncated cone-shaped end portion (30) capable of conveying the primary mixture directly to the combustion zone (6) facing the axial swirler (18), achieving efficient combustion even for primary mixtures comprising gases with a low calorific value.