Abstract: A novel sparse set membership NLMS （Normalized Least Mean Square） algorithm is proposed to address the existing sparse set-membership （SM） adaptive filtering algorithms， which generally has the problems of low stability of steady-state mean square deviation （MSD） and high operational complexity. The scheme proposes a zero-attraction （ZA） penalty function with lower computational complexity， which makes the algorithm more reasonable for estimation sparse channels. In a variety of sparse channel simulations， the proposed algorithm has lower steady-state MSD and higher stability compared to the current sparse setter algorithm. Finally， the proposed algorithm is applied to the sparse system identification of acoustic signals， which is more advantageous than the current sparse setter algorithm.