A bias‐compensated error‐modified normalised least‐mean‐square algorithm is proposed. The proposed algorithm employs nonlinearity to improve robustness against impulsive measurement noise, and introduces an unbiasedness criterion to eliminate the bias due to noisy inputs in an impulsive measurement noise environment. To eliminate the bias properly, a new estimation method for the input noise variance is also derived. Simulations in a system identification context show that the proposed algorithm outperforms the other algorithms because of the improved adaptability to impulsive measurement noise and input noise in the system.