Injecting supercritical CO₂ into underground reservoir space significantly alters the properties of the sequestered area, resulting in obvious time-lapse responses on post-stack seismic data. Time-lapse wave impedance inversion is an effective method to identify reservoir changes by calculating differential wave impedance with post-stack time-lapse differential data. Since reservoir parameters lapse are usually localized, the differential wave impedance often displays clear, block-like features, meaning that the reflectivity of differential wave impedance tends to exhibit sparsity. And due to the insufficient sparsity of the L₂ or L₁ regularization constraint term used in the conventional time-lapse wave impedance inversion method, it results in the problem of unclear boundary delineation in time-lapse difference imaging. In this paper, we propose to add L_1-2 norms with stronger sparsity-promoting characteristics as a prior constraint into the differential wave impedance inversion to enhance the clarity of the inversion results at the boundary clarity. The L_1-2 norm constraint improves the sharpness of the inversion results, especially at impedance interfaces. Through model testing and analysis, it is found that the L_1-2 norm constraint provides the highest inversion resolution in the vertical direction when compared to L₁ and L₂ norms. Additionally, in order to overcome the problem of poor transverse continuity of the inversion results that may be caused by using the single-channel inversion method, this paper adopts the f-x filtering method for result enhancement. By applying the proposed method to the model data and the CO₂ geological storage data in the deep saline layer of Sleipner, Norway, it is shown that the time-lapse wave impedance inversion method based on the constraints of L_1-2 norms can characterize the time-lapse seismic differential response efficiently and accurately, and it can be used as a means to monitor the CO₂ geological storage.