To improve the operation stability and anti-interference ability of oil-gas two-phase hydrodynamic seal, the response motion of its sealing compensation ring was studied, and the following dynamic characteristics of oil-gas two-phase hydrodynamic seal were revealed. Considered the comprehensive effect of temperature and deformation on sealing ring and fluid film, a finite element analysis model of fluid-solid-thermal coupling between sealing ring and fluid film was established by using MATLAB software. The dynamic stiffness and damping coefficients of the fluid film were calculated, the forced vibration model of the oil-gas two-phase dynamic pressure seal was solved, and the response motion of the compensating ring was analyzed. The effects of rotational speed, differential pressure, oil-gas ratio, spring stiffness and O-ring damping on the angular and axial amplitudes of motion response of the seal compensation ring were discussed, and the following dynamic characteristics of the seal are analyzed. The results show that the following dynamic characteristics of the seal can be improved by increasing the rotational speed and the oil-gas ratio. The increase of pressure difference, spring stiffness and O-ring damping is not conducive to the follow-up response motion of the compensating ring, in which the response amplitude of the compensating ring is insensitive to the change of spring stiffness and O-ring damping in the early period of increase, and the response amplitude of the compensating ring decreases sharply in the later period of increase. The research results provide theoretical support for the optimization of compensation mechanism and dynamic performance research of oil-gas two-phase hydrodynamic seals, and a method of solving the following dynamic characteristics of oil-gas two-phase hydrodynamic seals based on fluid-solid-thermal coupling is obtained.