Impedance inversion based on convolution models generally involves inversion of reflection coefficients before impedance inversion, and there are few studies that directly invert impedance using wave equations. Given that wave equation based methods have higher accuracy, this paper proposes a wave impedance inversion method based on wave equations. To ensure the lateral continuity of the impedance inversion model, Fourier series expansion is used in this paper to represent the wave impedance model using Fourier coefficients, which are used as inversion parameters; In the inversion process, an inversion strategy was designed to transition from low wave numbers to high wave numbers and to partition data groups. This not only ensures the inversion from the background wave impedance model to the fine wave impedance model, but also effectively avoids data redundancy, greatly improving computational accuracy and efficiency. The test results of synthetic seismic records and actual seismic data show that the method proposed in this paper has a significant ability to characterize the local edge features of "bead like" reservoirs, which can provide data support for the characterization and early reserve evaluation of fractured reservoirs.