Infrared sight axis stability framework is a three-degree-of-freedom frame structure. When the frames are in non-orthogonal positions, there will be a coupling phenomenon. This phenomenon will affect the stability accuracy of the system. The system of framework is modeled based on its kinetic equation, and it is pointed out that there is a complex non-linear coupling between the frameworks, and these disadvantages will produce a negative impact on the design of sight axis stabilization control system. Then it is proved that the system can be decoupled by the theorem in non-linear decoupling control system. The differential geometry method is used for decoupling the frameworks system. Experimental results show that this method can reduce the coupling impact between the frameworks when the framework of infrared sight axis stabilization system is in a non-orthogonal position, solve the problem that coupling movement makes the picture unstable, and improve the stability and reliability of system.