A headrest of adjustable height for a motor-vehicle seat

A headrest comprises: a support structure (12) adjustable in height by means of an actuator (18) and defining a curved surface (15) the convex side of which faces upwards, a pad (16) fixed to the backrest (10) at the front and slidable on the curved surface (15), and having a rear portion (16c) arranged for sliding vertically adjacent the rear (10b) of the backrest during the adjustment movement, and a guide device (20-22) for guiding the rear portion of the pad and keeping it oriented parallel to the backrest.