The invention relates to a support (10) for a headrest, comprising a tube leg (11) to which a head support part can be attached and having at least one free end (12a, 12b) for anchoring the support (10) in a seat fitting of an automobile seat, at least one reinforcing sleeve (15) being in the tube leg (11) for reinforcing at least one area (25) of the tube leg (11).The characterizing feature is that an outer surface (16) of the reinforcing sleeve (15) is in contact with an inner surface (17) of the tube leg (11) in a first circumferential region (T1) and that, in a second circumferential region (T2), the outer surface (16) has a groove (23) into which a ridge (22) projecting inward past the inner surface (17) engages.