Volume phase holographic (VPH) gratings are increasingly being used as diffractive elements in astronomical instruments due to their potential for very high peak diffraction efficiencies and the possibility of a compact instrument design when the gratings are used in transmission. Historically, VPH grating (VPHG) sizes have been limited by the size of manufacturer's holographic recording optics. We report on the design, specification and fabrication of a large, 290 mm × 475 mm elliptically-shaped, mosaic VPHG for the Apache Point Observatory Galactic Evolution Experiment (APOGEE) spectrograph. This high-resolution near-infrared multi-object spectrograph is in construction for the Sloan Digital Sky Survey III (SDSS III). The 1008.6 lines/mm VPHG was designed for optimized performance over a wavelength range from 1.5 to 1.7 μm. A step-and-repeat exposure method was chosen to fabricate a three-segment mosaic on a 305 mm × 508 mm monolithic fused-silica substrate. Specification considerations imposed on the VPHG to assure the mosaic construction will satisfy the end use requirements are discussed. Production issues and test results of the mosaic VPHG are discussed.