We present a detailed abundance analysis and atmospheric parameters of 76 stars from a survey to identify field Galactic red horizontal-branch (RHB) stars. High-resolution echelle spectra (R similar or equal to 60,000, S/N >= 100) were obtained with the 2.7 m Harlan J. Smith Telescope at McDonald Observatory. The target stars were selected only by color and parallax information. Overall metallicities and relative abundances of proton-capture elements (C, N, O, Li), alpha-elements (Ca and Si), and neutron-capture elements (Eu and La) were determined by either equivalent width or synthetic spectrum analyses. We used CN features at the lambda lambda 7995-8040 region in order to determine the C-12/C-13 ratios of our targets. Investigation of the evolutionary stages, using spectroscopic T-eff and log g values along with derived C-12/C-13 ratios, revealed the presence of 18 probable RHB stars in our sample. We also derived kinematics of the stars with available distance information. Taking into account both the kinematics and probable evolutionary stages, we conclude that our sample contains 5 thick-disk and 13 thin-disk RHB stars. Up until now, RHB stars have been considered as members of the thick disk, and were expected to have large space velocities and sub-solar metallicities. However, our sample is dominated by low-velocity solar-metallicity RHB stars; their existence cannot be easily explained with standard stellar evolution.