This brief proposes a novel normalized least mean square algorithm that is characterized by robustness against noisy input signals. To compensate for the bias caused by the input noise that is added at the filter input, a derivation method based on reasonable assumptions finds a bias-compensating vector. Moreover, the proposed algorithm has a fast convergence rate when applied to sparse systems, owing to its L₀-norm cost in the proposed update equation. The simulation results verify that the proposed algorithm improves the performance of the filter, in terms of system identification in sparse systems, in the presence of noisy input signals.