We present four epochs, A, B, C and D, of resolution ({lambda}/{delta}{lambda}) = 1200, 2.12 micron spectroscopy of the peculiar X-ray binary Cygnus X-3. About a half dozen spectra taken with resolution 900, and at 1.62 micron are also included. These data were obtained using the FSpec near-infrared spectrometer (Williams, D., Thompson, C.L., Rieke, G.H., Montgomery, E. 1993, Proc. SPIE 1308, 482) on the Multiple Mirror Telescope (MMT). The MMT is located at an elevation of 2600 m at the top of Mt. Hopkins in southern Arizona and is jointly operated by the Smithsonian Astrophysics Observatory and the University of Arizona. The spectra are stored as ascii files, listing wavelength in Angstroms and relative flux. Each file contains a five line header, giving the UT, Heliocentric Julian date and phase of the X-ray system at the start of the integration, followed by the data points. Additional information about the spectra can be obtained in the paper.