We present a measurement of metallicity in the Galactic center Quintuplet cluster made using quantitative spectral analysis of two luminous blue variables (LBVs). The analysis employs line-blanketed non-LTE wind/atmosphere models fit to high-resolution near-infrared spectra containing lines of H, He I, Si II, Mg II, and Fe II. We are able to break the H/He ratio versus mass-loss rate degeneracy found in other LBVs and to obtain robust estimates of the He content of both objects. Our results indicate solar iron abundance and roughly twice solar abundance in the α-elements. These results are discussed within the framework of recent measurements of oxygen and carbon composition in the nearby Arches cluster and iron abundances in red giants and supergiants within the central 30 pc of the Galaxy. The relatively large enrichment of α-elements with respect to iron is consistent with a history of more nucleosynthesis in high-mass stars than the Galactic disk.