Using a sample of nearly 140,000 primary red-clump stars selected from the LAMOST and Gaia surveys, we have identified a large sample of "young" [alpha/Fe]-enhanced stars with stellar ages younger than 6.0 Gyr and [alpha/Fe] ratios greater than 0.15 dex. The stellar ages and [alpha/Fe] ratios are measured from LAMOST spectra, using a machine-learning method trained with common stars in the LAMOST-APOGEE fields (for [alpha/Fe]) and in the LAMOST-Kepler fields (for stellar age). The existence of these "young" [alpha/Fe]-enhanced stars is not expected from the classical Galactic chemical evolution models. To explore their possible origins, we have analyzed the spatial distribution, and the chemical and kinematic properties of those stars and compared the results with those of the chemically thin and thick disk populations. We find that those "young" [alpha/Fe]-enhanced stars have distributions in number density, metallicity, [C/N] abundance ratio, velocity dispersion, and orbital eccentricity that are essentially the same as those of the chemically thick disk population. Our results clearly show those so-called "young" [alpha/Fe]-enhanced stars are not really young but genuinely old. Although other alternative explanations can not be fully ruled out, our results suggest that the most possible origin of these old stars is the result of stellar mergers or mass transfer.