Provided is a headrest moving device. When first and second gears, each of which has numerous teeth formed in widthwise and lengthwise directions, are engaged, the numerous widthwise teeth are engaged, and the numerous lengthwise teeth are engaged. Due to the teeth, it is possible to minutely adjust a position of a headrest and to withstand a high load. Even when some of the teeth are disengaged, the headrest moving device can be operated and provides excellent durability.