I present the discovery of Balmer-line absorption from H alpha to H9 in iron low-ionizaton broad absorption line (FeLoBAL) quasar, SDSS~J172341.10+555340.5 by near-infrared spectroscopy with the Cooled Infrared Spectrograph and Camera for OHS (CISCO) attached to the Subaru telescope. The redshift of the Balmer-line absorption troughs is 2.0530 +/- 0.0003, and it is blueshifted by 5370 km s^{-1} from the Balmer emission lines. It is more than $4000$ km s^{-1} blueshifted from the previously known UV absorption lines. I detect relatively strong (EW_rest=20A) [O III] emission lines which are similar to those found in other broad absorption line quasars with Balmer-line absorption. I derived a column density of neutral hydrogen of 5.2x10^{17} cm^{-2} by using the curve of growth and taking account of Ly alpha trapping. I searched for UV absorption lines which have the same redshift with Balmer-line absorption. I found Al II} and Fe III absorption lines at z=2.053 which correspond to previously unidentified absorption lines, and the presence of other blended troughs that were difficult to identify.
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