The present invention relates to a headrest moving device. Particularly, an elastic rib is disposed between a lock plate and a case, the elastic rib applies an elastic force to the lock plate in a direction different from a sliding direction of the lock plate, a curved part is formed between both ends of the elastic rib, the curved part is in contact with the case or the lock plate, and both ends of the elastic rib are spaced apart from a surface in contact with the curved part, and thus, there is no gap between the lock plate and the case, and the lock plate can be smoothly slid.