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In VTI media, the conventional inversion methods based on the existing approximation formulas are difficult to accurately estimate the anisotropic parameters of reservoirs, even more so for unconventional reservoirs with strong seismic anisotropy. Theoretically, the above problems can be solved by utilizing the exact reflection coefficients equations. However, their complicated expression increases the difficulty in calculating the Jacobian matrix when applying them to the Bayesian deterministic inversion. Therefore, the new reduced approximation equations starting from the exact equations are derived here by linearizing the slowness expressions. The relatively simple form and satisfactory calculation accuracy make the reduced equations easy to apply for inversion while ensuring the accuracy of the inversion results. In addition, the blockiness constraint, which follows the differentiable Laplace distribution, is added to the prior model to improve contrasts between layers. Then, the concept of GLI and an iterative reweighted least-squares algorithm is combined to solve the objective function. Lastly, we obtain the iterative solution expression of the elastic parameters and anisotropy parameters and achieve nonlinear AVA inversion based on the reduced equations. The test results of synthetic data and field data show that the proposed method can accurately obtain the VTI parameters from prestack AVA seismic data.