For a detailed analysis of stellar chemical abundances , high-resolution spectra in the optical have mainly been used , while the development of near-infrared ( NIR ) spectrograph has opened new wavelength windows . Red giants have a large number of resolved absorption lines in both the optical and NIR wavelengths , but the characteristics of the lines in different wave passbands are not necessarily the same . We present a selection of Fe i lines in the z ^ { \prime } , Y , and J bands ( 0.91–1.33 \mu m ) . On the basis of two different lists of lines in this range , the Vienna Atomic Line Database ( VALD ) and the catalog published by Meléndez & Barbuy in 1999 ( MB99 ) , we selected sufficiently strong lines that are not severely blended and compiled lists with 107 Fe i lines in total ( 97 and 75 lines from VALD and MB99 , respectively ) . Combining our lists with high-resolution ( \lambda / \Delta \lambda = 28 , 000 ) and high signal-to-noise ( > 500 ) spectra taken with a NIR spectrograph , WINERED , we present measurements of the iron abundances of two prototype red giants : Arcturus and \mu Leo . A bootstrap method for determining the microturbulence and abundance together with their errors is demonstrated . The standard deviations of \log \epsilon _ { Fe } values from individual Fe i lines are significantly smaller when we use the lines from MB99 instead of those from VALD . With the MB99 list , we obtained \xi = 1.20 \pm 0.11 { km~ { } s ^ { -1 } } and \log \epsilon _ { Fe } = 7.01 \pm 0.05 dex for Arcturus , and \xi = 1.54 \pm 0.17 { km~ { } s ^ { -1 } } and \log \epsilon _ { Fe } = 7.73 \pm 0.07 dex for \mu Leo . These final values show better agreements with previous values in the literature than the corresponding values we obtained with VALD .