We studied the near-infrared sky-brightness at J, H and Ks-bands as derived from the data taken during the first year and a half of routine science operations of the Large Binocular Telescope (LBT). This is the first comprehensive study of the near-infrared night sky-brightness ever conducted at the Mount Graham International Observatory (MGIO), based on a large dataset comprising 4699 near-infrared images taken in 52 nights. We analyzed the dependency of the near-infrared night sky-brightness with the airmass, the season and the moon phase and distance. The average night sky-brightnesses (dispersion) in the J, H and Ks bands scaled to the zenith is 15.82 mag/arcsec(2) (0.21), 14.29 mag/arcsec(2) (0.26) and 13.42 mag/arcsec(2) (0.32) respectively. Those values were derived for the first time at this observatory. At the J-band we found a tendency of the sky background to get darker by similar to 0.35 mag at the end of the night with respect to the evening twilight. Also in the J-band we found that the sky background can be up to similar to 0.11 mag brighter when observing at 10 degrees distance from the full moon. A correlation was also found between the night sky-brightness in the Ks-band and the air temperature with a gradient of -0.06 mag per 1 degrees C of temperature increase. If we compare the average sky brightness of the major observing sites we find that, at J-band, Mt. Graham is quite similar to the major sites but it quickly becomes the second darkest place at the H-band and definitely the darkest observing site at the Ks-band together with Mauna Kea. (C) 2013 Elsevier B.V. All rights reserved.