The present invention relates to a headrest moving device, and more particularly, to a headrest moving device in which one end of a strap is connected to a member to which a first member is connected, the other end of the strap is drawn out of a headrest or a seat, a guide rod configured to guide the strap is provided on the member to which the first member is connected, and a latching rod configured to latch a portion between one end and the other end of the strap is provided on the first member so that locking can be released through the strap drawn to the outside of the headrest. Thus, a user can easily recognize a way to release the locking and the first member can be smoothly rotated since the strap is smoothly guided.