Abstract: When propagating through subsurface viscoelastic media, seismic waves suffer from high-frequency energy attenuation and phase dispersion. Inverse Q filtering is a crucial method for restoring the broadband characteristics of seismic signals and enhancing resolution. However, since the amplitude compensation operator grows exponentially with frequency and traveltime, conventional inverse Q filtering is an ill-posed inverse problem, which is prone to numerical instability and high-frequency noise amplification. To address this issue, we formulate inverse Q filtering as a constrained optimization problem and propose a stable inverse Q filtering method based on an adaptive constraint of the attenuation operator. Based on the forward attenuation model, the critical attenuation boundary corresponding to the maximum allowable gain is taken as the stabilization criterion. Through nonlinear mapping, an analytical relationship between the attenuation operator and the stabilization constraint is established to realize continuous adjustment of the constraint according to the attenuation degree. A weak constraint is applied in the effective frequency band to preserve amplitude fidelity, while the stabilization constraint is enhanced in high-attenuation regions to suppress noise amplification. Synthetic and field data examples demonstrate that the proposed method yields improved numerical stability compared to conventional inverse Q filtering, enhancing the recovery of weak reflections to a certain extent and improving the imaging quality of deep targets.