An adaptive M-estimation algorithm based on set-membership filtering (SMF) is presented for robust filtering in impulsive noise. The proposed algorithm has unique features of data-dependent weights and selective update. It is derived from the general M-estimation and a SMF-type cost function. Simulation results show that the proposed algorithm performs much better than conventional recursive least-squares algorithms and conventional SMF algorithms in impulsive noise. Simulation results also demonstrate that the proposed algorithm has tracking capability superior to the least M-estimation approach, and it is more resistant to outliers.