This paper proposes a novel covariation approach for seismic wavelet estimation under the assumption that a real seismic signal follows non-Gaussian alpha-stable distributions. Since the non-Gaussian alpha-stable signals do not have finite second or higher order moments, the traditional methods of Gaussian distribution may not get a suitable solution. Based on the principle of fractional lower order statistics, the covariation approach deconvolution objective function matrix was given, and the details of wavelet estimation with the covariation approach were presented. Furthermore, computer simulation experiments on theoretical synthetic data and real seismic data were conducted. In the experiments, the effect of moments was considered. Among the estimated wavelets with different moments, the best wavelet should be the one with moment less than characteristic but close to characteristic. To verify the correctness and effectiveness of the proposed method, the extracted real wavelet was applied in real seismic acoustic impedance inversion. The result from the inversion of the 2-D real data set is consistent with the well log interpretation very well.