Method for manufacturing a gas burner of the type comprising a cup, provided with at least one tubular tapered part of a mixer with axial Venturi effect, and shaped to couple with a burner head provided with at least one flame-spreader, wherein said cup is made in a single piece by casting or die-casting in an apposite mold. Such a method comprises, in sequence, the following steps: a) arranging a mold with at least two shells, for casting or die-casting the afore said cup; b) arranging at least one core which could be removably inserted into the respective mold, which has at feast one jutting portion shaped with at least one tubular tapered part of the stickle of the afore said mixer with axial Venturi effect; c) inserting such a core into the mold and closing the afore said at least two mold shells so that the afore said at least one jutting portion of the core is retained, at least partially, at a distance from the opposite inner walls of the closed mold; the core and the mold being shaped so that at least one ending part of such a core replaces, at least partially, part of the perimetrical area of the cup defined by the mold; d) pouring or pressure-injecting molten metal material into the closed mold; e) opening the mold, drawing out the afore said core and then removing the die formed cup after the metal material is solidified; f) applying at least one closing plug to the side hole (or side holes) of the die formed cup which corresponds/correspond to the ending part of the core which replaced part of the perimetrical area of the cup in the mold.