Using a parallel three-shaft coupling rotor system with two pairs of helical gears as the research object, a meshing dynamic model with a general total degree of freedom is established by considering the effects of the static transmission error and the geometric eccentricity of the gears. Combined with the dynamic model, a finite element model of the rotor system is determined. In this model, the rotor system is simulated using a beam element, and the gear pair is simulated using a mesh stiffness matrix and damping matrix. Finally, considering the different degrees of freedom coupling of the system, the dynamic characteristics of the system are analyzed. The results show that more coupling natural frequencies of the system can be obtained by considering bending-torsional coupling and bending-torsional-axial-swing coupling. All peaks of the response calculation results correspond to the natural frequencies of the system, and the bending-torsional-axial-swing coupling is a more effective way to analyze the dynamic characteristics of the system. The results are beneficial to the structural design of gear coupled rotor systems.