Quantitative inversion of fracture weakness plays an important role in fracture prediction. Considering reservoirs with a set of vertical fractures as horizontal transversely isotropic media, the logarithmic normalized azimuthal elastic impedance (EI) is rewritten in terms of Fourier coefficients (FCs), the 90° ambiguity in the azimuth estimation of the symmetry axis is resolved by judging the sign of the second FC, and we choose the FCs with the highest sensitivity to fracture weakness and present a feasible inversion workflow for fracture weakness, which involves: (1) the inversion for azimuthal EI datasets from observed azimuthal angle gathers; (2) the prediction for the second FCs and azimuth of the symmetry axis from the estimated azimuthal EI datasets; and (3) the estimation of fracture weakness combining the extracted second FCs and azimuth of the symmetry axis iteratively, which is constrained utilizing the Cauchy sparse regularization and the low-frequency regularization in a Bayesian framework. Tests on synthetic and field data demonstrate that the 90° ambiguity in the azimuth estimation of the symmetry axis has been removed, and reliable fracture weakness can be obtained when the estimated azimuth of the symmetry axis deviates less than 30°, which can guide the prediction of fractured reservoirs.