We are designing a sensitive high resolution (R=60,000-100,000) spectrograph for the Giant Magellan Telescope (GMTNIRS, the GMT Near-Infrared Spectrograph). Using large-format IR arrays and silicon immersion gratings, this instrument will cover all of the J (longer than 1.1 μm), H, and K atmospheric windows or all of the L and M windows in a single exposure. GMTNIRS makes use of the GMT adaptive optics system for all bands. The small slits will offer the possibility of spatially resolved spectroscopy as well as superior sensitivity and wavelength coverage. The GMTNIRS team is composed of scientists and engineers at the University of Texas, the Korea Astronomy and Space Science Institute, and Kyung Hee University. In this paper, we describe the optical and mechanical design of the instrument. The principal innovative feature of the design is the use of silicon immersion gratings which are now being produced by our team with sufficient quality to permit designs with high resolving power and broad instantaneous wavelength coverage across the near-IR.