The IGRINS (Immersion GRating INfrared Spectrometer) is a high resolution wide-band infrared spectrograph developed by Korea Astronomy and Space Science Institute (KASI) and the University of Texas at Austin (UT). Immersion grating is a key component of IGRINS, which disperses the input ray by using a Silicon material with a lithography technology. Opto-mechanical mount for the immersion grating is important to keep the high spectral resolution and the optical alignment in a cold temperature of $130{pm}0.06K$. The optical performance of immersion grating can maintain within the de-center tolerance of ${pm}0.05mm$ and the tip-tilt tolerance of ${pm}1.5arcmin$. The mount mechanism utilizes the flexure and the kinematic support design to satisfy the requirement and the operation condition. When the IGRINS system is cooled down to a cold temperature, three flexures compensate the thermal contraction stress due to the different material between the immersion grating and the mounting part(Aluminum 6061). They also support the immersion grating by an appropriate preload. Thermal stability is controlled by a copper strap with proper dimensions and a heater. Generally structural and thermal analysis was performed to confirm the mount mechanism. This talk presents the opto-mechanical mount design of the immersion grating of IGRINS.