Power-line communications (PLC) commonly employs orthogonal frequency-division multiplexing (OFDM) as the modulation technique, and impulsive noise has a significant negative impact on its performance. Using the property of null subcarriers in OFDM and the fact that impulsive noise is sparse, we formulate a minimization problem to detect and estimate the impulsive noise. In previous works, ℓ1-norm minimization was employed to achieve this task. In this paper, we propose to use a smoothed ℓ0-norm minimization algorithm for impulsive noise detection instead. Simulation results show that this approach is promising as it achieves comparable performance as ℓ1-norm minimization but with much lower complexity.