A large sample survey of Galactic red horizontal-branch (RHB) stars was conducted to investigate their atmospheric parameters and elemental abundances. High-resolution spectra of 76 Galactic field stars were obtained with the 2.7 m Smith Telescope at McDonald Observatory. Only the color and the parallax were considered during the selection of the field stars. Equivalent width or synthetic spectrum analyses were used in order to determine the relative abundances of the following elements: proton-capture elements C, N, O and Li, alpha-elements Ca and Si, and neutron-capture elements Eu and La. Additionally, C-12/C-13 isotopic ratios were derived by using the CN features mainly located in the 7995 - 8040 spectral region. The evaluation of effective temperatures, surface gravities and C-12/C-13 isotopic ratios together with evolutionary stages of the candidates revealed that 18 out of 76 stars in our sample are probable RHBs. Including both kinematic and evolutionary status information, we conclude that we have five thick disk and 13 thin disk RHB stars in our sample. Although RHB stars have been regarded as thick disk members of the Galaxy, the low-velocity RHBs with a solar metallicity in our sample suggests the existence of a large number of thin disk RHBs, which cannot be easily explained by standard stellar evolutionary models.