Abstract: The unique motion of binary asteroid systems provide important clues for the evolution of planets. Therefore, binary asteroid systems become hot targets in asteroid exploration. In this paper, based on the double ellipsoid model, the relative motion, equilibrium condition and stability of binary asteroid systems are studied. Firstly, the full two-body dynamic equation of the double ellipsoid model is established to describe the relative motion of a binary asteroid system. Secondly, the Lagrangian equation of motion is used to solve the angular momentum and energy of the system, and the equilibrium conditions are obtained. Finally, a method to determine the stability of equilibrium is given by using the zero-velocity state surface and the influence of the asteroid's physical parameter on the stability of equilibrium is analyzed. This research can provide a theoretical reference for the trajectory design and control in future exploration missions to binary asteroid systems.