We present a chemical abundance analysis of the secondary star in the black hole binary V404 Cygni, using Keck I/High Resolution Spectrometer. We adopt a χ2-minimization procedure to derive the stellar parameters, taking into account any possible veiling from the accretion disk. With these parameters we determine the atmospheric abundances of O, Na, Mg, Al, Si, Ca, Ti, Fe, and Ni. The abundances of Al, Si, and Ti appear to be slightly enhanced when comparing with average values in thin-disk solar-type stars. The O abundance, derived from optical lines, is particularly enhanced in the atmosphere of the secondary star in V404 Cygni. This, together with the peculiar velocity of this system as compared with the Galactic velocity dispersion of thin-disk stars, suggests that the black hole formed in a supernova (SN) or hypernova (HN) explosion. We explore different SN/HN models having various geometries to study possible contamination of nucleosynthetic products in the chemical abundance pattern of the secondary star. We find reasonable agreement between the observed abundances and the model predictions. However, the O abundance seems to be too high regardless of the choice of explosion energy or mass cut, when trying to fit other element abundances. Moreover, Mg appears to be underabundant for all explosion models, which produces Mg abundances roughly two times higher than the observed value.