Prolonged exposure of the human arm to vibrations from hand-held impact (HIM) tools can be hazardous as such, it is important that the level of vibration suppression in HIMs is improved. This paper sought to address this issue by studying a model of the hand-arm system (HAS) coupled to a HIM which is also coupled to a nonlinear tuned vibration absorber inerter (NVAI). The HAS is modelled as a 2-DOF system coupled to the HIM at a single point. The HIM is modelled as an oscillator with linear damping, and both linear and nonlinear stiffnesses. The nonlinear stiffness of the HIM is introduced to represent the nonlinearities introduced by the vibro-impact dynamics of the HIM. After obtaining the equations of motion for the system, an analytical solution is obtained using the harmonic balance method. The analytical solution is validated using direct numerical integration and the results show very good agreement. The performance of the NVAI is compared to those of the classical nonlinear and linear vibration absorbers. Parametric study is carried out to examine the role of key design parameters, such as the damping of the absorber, nonlinear stiffness of the HIM and inertance of the NVAI, on the performance of the NVAI.