We have derived elemental abundances of three field red horizontal branch stars using high-resolution (R similar or equal to 45,000), high signal-to-noise ratio (S/N greater than or similar to 200) H-and K-band spectra obtained with the Immersion Grating Infrared Spectrograph (IGRINS). We have determined the abundances of 21 elements, including alpha (Mg, Si, Ca, S), odd-Z (Na, Al, P, K), Fe-group (Sc, Ti, Cr, Co, Ni), neutron-capture (Ce, Nd, Yb), CNO-group elements. S, P, and K are determined for the first time in these stars. H- and K-band spectra provide a substantial number of S I lines, which potentially can lead to a more robust exploration of the role of sulfur in the cosmochemical evolution of the Galaxy. We have also derived C-12/C-13 ratios from synthetic spectra of the first-overtone (CO)-C-12 (2-0) and (3-1) and (CO)-C-13 (2-0) lines near 23440 angstrom and (CO)-C-13 (3-1) lines at about 23730 angstrom. Comparison of our results with the ones obtained from the optical region suggests that the IGRINS high-resolution H- and K-band spectra offer more internally self-consistent line abundances of the same species for several elements, especially the alpha-elements. This in turn provides more reliable abundances for the elements with analytical difficulties in the optical spectral range.