Xu, Y.P.. Zhang, K., Li, Z.C., He. Z.L.. Wang, J.C. and Gao, J.F., 2022. Full waveform inversion of viscoelastic medium based on gradient preprocessing. Journal of Seismic Exploration, 31: 579-596. The subsurface medium exists mainly in a viscoelastic form, and there are two phenomena: amplitude attenuation and phase dispersion. However, the full waveform inversion is used to inverse the subsurface medium parameters in a large scale way, and the phase dispersion phenomenon is more often solved by migration. Therefore, we investigate the Kelvin-Voigt model with only amplitude attenuation. In this paper, we derive the back propagation wavefield formulation and gradient formulation for full waveform inversion of viscoelastic media based on the Kelvin-Voigt model, and analyze the correctness and feasibility of the method. Also, in viscoelastic media, low velocity geological bodies may cause the gradient of the full waveform inversion to fall into local convergence. It is shown that the gradient preprocessing method based on the pseudo-Hessian operator can suppress the gradient from falling into local convergence. Therefore, this manuscript incorporates a pseudo-Hessian operator for gradient preprocessing and derives a gradient preprocessing formulation for full waveform inversion of viscoelastic media based on gradient preprocessing, which solves the problem that the inversion gradient falls into local convergence. It is demonstrated through examples that the method can solve the problem of the inversion gradient falling into local convergence caused by the low-velocity body in the full waveform inversion of viscoelastic media.