Power line communication is severely affected by impulsive noise, especially asynchronous impulsive noise with high power spectral density and short duration. This paper presents an asynchronous impulsive noise suppression method in power line communication system. Based on the component of the asynchronous impulsive noise and the background noise extracted from the received signal by using a null subcarrier matrix, a sparse iterative covariance estimation method is proposed. A optimization problem for estimating impulsive noise power is formed based on a minimum covariance matrix fitting criterion, and the impulsive noise power is then obtained by an iterative algorithm. After that, the impulsive noise is estimated by using the linear minimum mean square estimate method and subtracted from the received signal. Finally, simulation results show that the proposed method can achieve better performance in terms of bit error rate, and has lower computational complexity.