To study the association relationship between amplitude jumps and tooth meshing impact in a gear transmission system with backlash, the dynamic equations of amplitude-frequency characteristics of a single gear system are established by the method of harmonic balance. The equation is solved by the quasi-Newton Broyden rank-2 method and pseudo-arc-length continuation algorithm, and then, the two-dimensional domain boundary solution structure of amplitude-frequency characteristics is obtained. The multi-valued solution and tooth surface impact characteristics of the system in the parameter domain boundary structure of the backlash, static comprehensive error, time-varying meshing stiffness, damping, and frequency are analyzed, respectively. The effects of parameters on amplitude jump, multi-value solution, and tooth surface impact characteristics of the system are investigated. The analysis shows that the amplitude jump response of the system appears near the resonance frequency. The nonlinear jump also appears at the non-clearance bearing supports due to the effect of the gear backlash. When b＞1.55, the backlash is not sensitive to the system multi-value solution and tooth surface impact characteristics. The multi-value solution and tooth surface impact characteristics of the system are exacerbated by the increase of the meshing stiffness and the static comprehensive error. Damping can effectively suppress the system amplitude jump and tooth surface impact characteristics, when ξ＞ 0.3, the system shows linear characteristics.