To achieve precise generation of high-impact waveforms for applications such as aviation safety testing, this paper investigates the mechanism for controlling impact waveforms in graded foam metals under different boundary conditions. Based on the laws of mass and momentum conservation, a theoretical model for impact waveform generation in graded foam metals under free and elastic boundaries is established. Furthermore, an inverse design method for density gradients is proposed, which integrates average relative density constraints with the Gauss-Newton iteration method, enabling the inverse solution from a target acceleration waveform to the corresponding material density distribution. Finite element results demonstrate that this method can effectively generate target waveforms, such as triangular and half-sine waves, under various boundary conditions. The study also reveals that: the free boundary is more suitable for simulating high-amplitude, wide-pulse waveforms, while the elastic boundary can improve the feasibility of low-amplitude waveforms through stiffness regulation. Although the boundary condition does not affect the impact duration, it significantly influences the waveform shape. In addition, excessive impedance mismatch between adjacent segments can lead to increased waveform fluctuations, thereby compromising waveform generation accuracy. The proposed density gradient inverse design strategy demonstrates general applicability, providing both a theoretical support and a practical design tool for the independent development of high-impact testing technologies.