Airborne photoelectric stabilization platform is one of the most effective devices to isolate aircraft motion from tracking and scanning equipment. In order to make the airborne photoelectric stabilization platform lighter in weight and better in performance, a four-claw spherical stabilization platform is designed. The multi-body dynamic analysis of the four-claw spherical stabilized platform is carried out to verify whether the designed platform meets the functional requirements, that is, whether the four-claw spherical platform can isolate the movement of aircraft and whether the spherical platform can rotate around the pitch axis and azimuth axis. SolidWorks software is used to build a three-dimensional model of a four-claw spherical stabilized platform. Then simplify the three-dimensional model of the platform, import Adams software, carry out multi-body dynamic analysis of a four-claw spherical stabilized platform, verify whether the platform can meet the function. The analysis results show that the designed four-claw spherical stabilized platform can isolate the motion of the aircraft and rotate around the azimuth axis and pitch axis to meet the function, which provides a reference for the design of similar platforms.