The Long-wave Infrared Spatial Heterodyne Interferometer may have interference fringe distortion due to non-uniform stress acting on the optical components under cryogenic conditions， which will cause performance degradation of the interferometer system. To solve the problem of interference fringe distortion under cryogenic conditions， this paper analyzed the factors affecting interference fringe distortion based on the initial optical mechanical system of Long-wave infrared spatial heterodyne interferometer， and combined the optical-mechanical-thermal coupling analysis method to simulate the cryogenic state of the interferometer system. Then， a cryogenic micro-stress dynamic stable installation structure was designed for grating， which is the key component affecting fringe distortion. After the optimization of structure， the Root-Mean-Square（RMS） and Peak-to-Valley（PV） values of grating’s surface shape are 3.89×10^-2 nm and 2.21×10^-1 nm， respectively， which are five orders of magnitude lower than the initial structure analysis results. The simulated interference fringe distortion is less than 1 detector pixel. The cryogenic verification test of whole system shows that the optimized structure can effectively reduce the distortion of interference fringe， and the distortion is less than 2 detector pixels. The experimental results are highly consistent with the simulation results， which verifies the effectiveness of the optimization analysis method. The optimization analysis method has great significance and value for improving the structural stability and operating performance of the cryogenic reflective optical system.