Aiming at the influence of parameter uncertainty on gear system, an uncertainty interval analysis method based on Chebyshev polynomials is employed to analyze the dynamic characteristics of gear system with parameter uncertainty. In this paper, the complete tooth profile curve is considered, and the potential energy method is employed to calculate the timevarying mesh stiffness of both healthy and cracked tooth. On this basis, a six degree of freedom lumped-parameter gear system model is established. The uncertainties of parameters such as gear mass, bearing support stiffness, and Young's modulus are considered. The influence of these uncertainties on the vibration response of healthy gear system is analyzed through numerical simulation. Furthermore, the interval response of an uncertain gear system with root crack faults is investigated, taking into account the impact of cracks.The results show that the gear meshing stiffness decreases with the increase of crack depth. Under the influence of uncertain parameters, phenomena such as “frequency shift”and “resonance band” will occur in the system, weakening the stability of the system.