Method for laser welding a first and a second workpiece portion (61, 62) by means of a laser beam, which is guided along a joining gap formed between the workpiece portions (60, 61) by a laser processing head and in which the laser beam is focused with a processing optical system, and in which an additional substance having a supply device is aligned in relation to the joining gap, - at least one gap width of the joining gap of the workpiece portions (61, 62) to be welded is detected characterised by the use of a control device (31, 32), which is provided for controlling the following steps, - that the detected gap width is evaluated along the course of the joining gap and is compared with at least one first and one second gap size, wherein the first gap size comprises a gap width, in which a welded seam is formed without the additional substance and the second gap size comprises a gap width, with which an additional substance is supplied for the formation of the welded seam for filling the joining gap, - that with a detected gap width, which is within the first gap size, the supply of the additional substance to the joining gap is shut down during the laser welding, and a beam profile of the laser beam is set with a point or ring focus (43, 46), - that with a detected gap width, which is within the second gap size, a supply of the additional substance to the joining gap is controlled, and a beam profile of the laser beam is set with a ring focus, and - that an annular beam surface is formed by the beam profile of the laser beam having a ring focus, said beam surface covering the joining gap, wherein an inner beam-free region is delimited by an inner beam surface edge, said region substantially corresponding to the width of the joining gap or being formed wider, and an outer beam surface edge of the annular beam surface covering the two edges of the workpiece portions (61, 62) to be welded. - at least one gap width of the joining gap of the workpiece portions (61, 62) to be welded is detected characterised by the use of a control device (31, 32), which is provided for controlling the following steps, - that the detected gap width is evaluated along the course of the joining gap and is compared with at least one first and one second gap size, wherein the first gap size comprises a gap width, in which a welded seam is formed without the additional substance and the second gap size comprises a gap width, with which an additional substance is supplied for the formation of the welded seam for filling the joining gap, - that with a detected gap width, which is within the first gap size, the supply of the additional substance to the joining gap is shut down during the laser welding, and a beam profile of the laser beam is set with a point or ring focus (43, 46), - that with a detected gap width, which is within the second gap size, a supply of the additional substance to the joining gap is controlled, and a beam profile of the laser beam is set with a ring focus, and - that an annular beam surface is formed by the beam profile of the laser beam having a ring focus, said beam surface covering the joining gap, wherein an inner beam-free region is delimited by an inner beam surface edge, said region substantially corresponding to the width of the joining gap or being formed wider, and an outer beam surface edge of the annular beam surface covering the two edges of the workpiece portions (61, 62) to be welded.