In prestack seismic data, outlier errors occur and can negatively influence the outcome of the amplitude-versus-angle (AVA) inversion process. Hence, their effect needs to be minimized during AVA inversion. AVA inversion based on the -norm-based likelihood function is highly sensitive to outlier errors. In comparison, AVA inversion based on the -norm-based likelihood function is less affected by outlier errors, and for this reason we have used it with the total variation regularization method used as a constraint to invert discontinuities from geologic bodies. To ensure that the inversion results contain low-frequency components, prior information constraints from model parameters are added to the inverse objective function, which is then solved by the iterative reweighted least-squares method. Results of numerical tests and real-data examples from the application of this method indicate that the algorithm is strongly robust against noise, especially abnormal outlier errors, and that the results of the inversion are reasonable.