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With the development of new energy technology, the number of electric vehicles (EVs) will continue to increase, which will seriously threaten the safe operation of the power grid. The V2G information interaction system can help the power grid to achieve safe and reliable operation. Therefore, under the framework of the V2G information interaction system, this paper establishes the communication system between EVs and charging piles based on power line communication (PLC), which can reduce the cost and avoid the problem that the incompatible communication interface caused by different specifications of charging piles. Due to the severe impulse noise (IN) communication environments between EVs and charging piles, the transmission performance would be seriously degraded. Hence, an improved-priori-aided sparsity adaptive matching pursuit (IPA-SAMP) is proposed to reconstruct IN. In the process of IN cancellation, the measurement vector is obtained from the null sub-carriers. In order to efficiently reconstruct IN, as the input of the IPA-SAMP algorithm, partial support are improved by the optimized threshold, which significantly improve the accuracy and robustness of the recovered IN. The proposed IPA-SAMP algorithm can effectively recover IN in the channel between EVs and charging piles, improves the reliability of the information exchange system, which is validated by computer simulations.