We discuss the optical design of an infrared multi-object spectrograph (MOS) concept that is designed to take advantage of the multi-conjugate adaptive optics (MCAO) corrected field at the Gemini South telescope. This design employs a unique, cryogenic MEMS-based focal plane mask to select target objects for spectroscopy by utilizing the Micro-Shutter Array (MSA) technology originally developed for the Near Infrared Spectrometer (NIRSpec) of the James Webb Space Telescope (JWST). The optical design is based on all spherical refractive optics, which serves both imaging and spectroscopic modes across the wavelength range of 0.9−2.5 μm. The optical system consists of a reimaging system, MSA, collimator, volume phase holographic (VPH) grisms, and spectrograph camera optics. The VPH grisms, which are VPH gratings sandwiched between two prisms, provide high dispersing efficiencies, and a set of several VPH grisms provide the broad spectral coverage at high throughputs. The imaging mode is implemented by removing the MSA and the dispersing unit out of the beam. We optimize both the imaging and spectrographic modes simultaneously, while paying special attention to the performance of the pupil imaging at the cold stop. Our current design provides a 1' ♦ 1' and a 0.5' ♦ 1' field of views for imaging and spectroscopic modes, respectively, on a 2048 × 2048 pixel HAWAII-2RG detector array. The spectrograph’s slit width and spectral resolving power are 0.18'' and 3,000, respectively, and spectra of up to 100 objects can be obtained simultaneously. We present the overall results of simulated performance using optical model we designed.