An automatic moving apparatus may include a collision prediction sensor, a control unit comparing a value measured by the collision prediction sensor, with a reference value stored in the control unit, and outputting a control signal when it may be determined that the value measured by the collision prediction sensor is higher than the reference value, and a headrest moving unit moving a headrest unit toward a passenger's head before the headrest unit comes into contact with the passenger's head, and including a stay rod connected to the headrest unit, both sides of the stay rod being placed in a vertical direction, tilting device tilting the stay rod forwards or backwards relative to a seatback in response to the control signal of the control unit, and vertical moving device moving the stay rod in a vertical direction in response to the control signal of the control unit.