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An equalization algorithm is proposed to guarantee a stable performance in fast fading channels for the advanced television system committee (ATSC) digital television (DTV) systems, in channels with high Doppler shifts, the conventional equalizer shows severe performance degradation. The conventional equalizer with long filter taps to overcome long delay profiles is 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 an equalizer initialization. Fast fading channels with high Doppler shifts can be compensated with an adaptive 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.