The circumferential rod-fastening rotor is composed of multiple disks fastened together by preload provided by tie rods evenly distributed along the circumference of rotor. After the rotor has been running for a period of time, some tie rods will loosen and fail to provide preload due to thermal load, centrifugal load, etc. Which causes the preload that was originally evenly distributed in the circumferential direction to become uneven. Uneven preload introduces anisotropy of contact interface stiffness between rotor disks and generalized bending moments, which have important effects on nonlinear dynamic characteristics of rotor-bearing-seal system. Further, it is common for multiple tie rods to become loose at the same time in practical engineering, the relative position of loose tie rods in the circumferential direction will also have an important impact on rotor dynamics. The relevant research has not been done yet. In this paper, a contact model of the rough machined surface is firstly established by combining the statistical contact theory and fractal contact theory, and then the contact stiffness model between disks is established based on the contact model. Finally, the dynamic model of the circumferential rod-fastening rotor-bearing-seal system is established and solved. The effect of relative phase of loose tie rods on the nonlinear dynamic characteristics of rod-fastening rotor-bearing-sealing system is studied. It can be concluded that relative phase of the loose tie rod has an important influence on the frequency, bifurcation, and periodic motion of the rotor system. At lower speed, the anisotropy of contact stiffness caused by loose rods has little effect on the rotor trajectory, while the generalized bending moment has a greater influence on dynamics of the system. At higher speed, the anisotropy of contact stiffness has a great influence on the axis rail of the rod-fastening rotor.