Abstract Objective. Ultrasound attenuation coefficient estimation (ACE) has diagnostic potential for clinical applications such as quantifying fat content in the liver. Previously, we have proposed a system-independent ACE technique based on spectral normalization of different frequencies, called the reference frequency method (RFM). This technique does not require a well-calibrated reference phantom for normalization. However, this method may be vulnerable to severe reverberation clutter introduced by the body wall. The clutter superimposed on liver echoes may bias the estimation. Approach. We proposed to use robust principal component analysis, combined with wavelet-based sparsity promotion, to suppress the severe reverberation clutters. The capability to mitigate the reverberation clutters was validated through phantom and in vivo studies. Main Results. In the phantom studies with added reverberation clutters, higher normalized cross-correlation and smaller mean absolute errors were attained as compared to RFM results without the proposed method, demonstrating the capability to reconstruct tissue signals from reverberations. In a pilot patient study, the correlation between ACE and proton density fat fraction (PDFF), a measurement of liver fat by MRI as a reference standard, was investigated. The proposed method showed an improvement of the correlation (coefficient of determination, R = 0.82) as compared with the counterpart without the proposed method (R = 0.69). Significance: The proposed method showed the feasibility of suppressing the reverberation clutters, providing an important basis for the development of a robust ACE with large reverberation clutters.