We present the discovery of Balmer line absorption from H \alpha to H \gamma in an iron low-ionization broad absorption line ( FeLoBAL ) quasar SDSS J152350.42+391405.2 ( hereafter SDSS J1523+3914 ) , by the quasi-simultaneous optical and near-infrared spectroscopy . The Balmer line absorption is at z _ { absor } = 0.6039 \pm 0.0021 and blueshifted by v = 10 , 353 km s ^ { -1 } with respect to the Balmer emission lines . All Balmer BALs have uniform absorption profile with the widths of \Delta v \sim 12,000 km s ^ { -1 } . We also found the absorption trough in He i* \lambda 10830 with the same velocity and width in the H -band TripleSpec spectrum of SDSS J1523+3914 . This object is only the tenth active galactic nucleus known to exhibit non-stellar Balmer absorption , and also the case with the highest velocity and broadest Balmer absorption lines which have ever been found . A CLOUDY analysis shows that the absorbers require an gas density of { log _ { 10 } } ~ { } n _ { e } ~ { } ( { cm ^ { -3 } } ) = 9 and an ionization parameter of { log _ { 10 } } ~ { } U = -1.0 . They locate at a distance of \sim 0.2 pc from the central ionizing source which is slightly farther than that of BELRs . Furthermore , SDSS J1523+3914 is one of the brightest Balmer-BAL quasar ever reported , with unique iron absorption variations , making it as the most promising candidate for follow up high-resolution spectroscopy , multi-band observations , and long-term monitoring .