A robot binding apparatus for coil packaging includes: a grip unit that grips a band used for packaging a coil; a grip robot that supports the grip unit, rotates the grip unit seizing the band at the periphery of the coil to make the band wound on the coil, and moves the band to a fastening position; a head unit that provides the band to the grip unit and fastens the band at the band fastening position; and a head robot that supports the head unit and moves the head unit to the band fastening position.