The present invention relates to a headrest moving device. The headrest moving device includes an ejector casing mounted to a seat frame, a tiltable member tiltably installed in the ejector casing, a stay rod connected to a headrest and passing through the tiltable member, a movable unit having a connector and a mounting holder rotatably coupled to the connector and connected to the stay rod, a screw engaged with the connector in a screw manner of engagement, and a motor for rotating the screw, wherein the tiltable member can be tilted relative to the ejector casing and the mounting holder can be rotated relative to the connector, so that the headrest moving device can easily move the headrest forwards and upwards.