Impulsive noise (IN) is the most dominant factor degrading the performance of communication systems over powerlines. In order to improve performance of high-speed power line communication (PLC), this work focuses on mitigating burst IN effects based on compressive sensing (CS), and an adaptive burst IN mitigation method, namely combination of adaptive interleaver and permutation of null carriers is designed. First, the long burst IN is dispersed by an interleaver at the receiver and the characteristic of noise is estimated by the method of moment estimation, finally, the generated sparse noise is reconstructed by changing the number of null carriers(NNC) adaptively according to noise environment. In our simulations, the results show that the proposed IN mitigation technique is simple and effective for mitigating burst IN in PLC system, it shows the advantages to reduce the burst IN and to improve the overall system throughput. In addition, the performance of the proposed technique outpeformences other known nonlinear noise mitigation methods and CS methods.