An asynchronous impulsive noise mitigation algorithm is proposed for power line communication (PLC) systems. Multiple techniques have been proposed in the literature in order to mitigate asynchronous impulsive noise to enable PLC, e.g., in smart grid applications. Most of the schemes proposed so far are based on non-linear methods, such as clipping and nulling. Even though these non-linear schemes reduce bit error rate (BER) by a significant amount, it will be shown in this paper that they can be easily outperformed by the proposed linear method.The performance improvement of the proposed algorithm comes from the fact that the identification of true locations of impulsive noise samples is very accurate, so that the reduction of the impulsive noise is only carried out at the truly contaminated samples of the received signal. This approach avoids typical problems encountered in clipping and nulling algorithms, where samples besides the ones containing the impulsive noise are also affected, thus creating additional distortion in the received signal. The superior performance of the proposed scheme is demonstrated via numerical simulations.