The results of a comparative analysis of the elemental abundances in the atmospheres of 14 red giants with high Galactic space velocities are presented. For almost all of the chemical elements considered, the their abundance trends with metallicity correspond to those constructed for thick-disk dwarfs. In the case of sodium, the main factor affecting the [Na/Fe] abundance in the stellar atmosphere for red giants is the surface gravity that characterizes the degree of development of the convective envelope. The difference between the [Na/Fe] abundances in the atmospheres of thin- and thick-disk red giants has been confirmed.