Considering that there is a lack of anti-noise interference measures in adaptive OFDM system of medium voltage power line communication, a low complexity subspace iterative algorithm is proposed to suppress background noise. The feature space of the noisy OFDM signal is decomposed based on the subspace theory, and under the constraint of minimum signal distortion, the best estimate of the ideal signal is obtained by applying the Lagrangian optimal extremum method. For the high computational complexity of eigenvalue decomposition of the classical subspace method, the repeated one-dimensional subspace iteration is used to reduce the computational complexity. An adaptive OFDM system which combining the signal-to-noise ratio threshold and water injection principle is constructed, and the system performances before and after background noise suppression are compared.. The results show that, the method can further improve the bit error rate performance and improve the signal-to-noise ratio, and the method proposed in this paper can be used to optimize the application of adaptive OFDM systems of PLC.