An equalization algorithm is proposed to guarantee a stable performance in fast fading channels for digital television (DTV) systems from the advanced television system committee (ATSC) standard. In channels with high Doppler shifts, the conventional equalization algorithm shows severe performance degradation. Although the conventional equalizer compensates poor channel conditions to some degree, long filter taps required to overcome long delay profiles are not suitable for fast fading channels. The Proposed sparse equalization algorithm is robust to the multipaths with long delay Profiles as well as fast fading by utilizing channel estimation and equalizer initialization. It can compensate fast fading channels with high Doppler shifts using a filter tap selection technique as well as variable step-sizes. Under the ATSC test channels, the proposed algorithm is analyzed and compared with the conventional equalizer. Although the proposed algorithm uses small number of filter taps compared to the conventional equalizer, it is stable and has the advantages of fast convergence and channel tracking.