Abstract: This paper applied a polyhedron-ellipsoid model to study the dynamics of resonant orbits near the binary system, with the binary system 66391 Moshup as an example. A series of resonant orbital families were calculated the shooting method and continuation method, and the stability and bifurcation of the orbital families were analyzed. Finally, homoclinic connections between resonant orbits were computed by using invariant manifolds. The research shows that no strict planar resonant orbit exists because of the asymmetry of the gravitational field, and the orbital stability and bifurcation have also been affected. In addition, the availability of designing transfer trajectories through resonant orbits was also demonstrated.