Power line communications (PLC) play an important role in smart grid for its cost efficiency. However, the power line is not designed for communication purposes so that its communication environment is hostile with formidable obstacles such as frequency selective fading and impulsive noise. A number of existing methods have been used to deal with the challenges of PLC. Nevertheless, most of existing technologies can only solve part of the problems. This paper presents a multiple access system, namely orthogonal frequency division multiplexing interleave division multiple access (OFDM-IDMA), which is feasible in PLC for it can solve the problems caused by both frequency selective fading channel and impulsive noise. Analytical error performance and the corresponding lower bound are derived for our proposed OFDM-IDMA over frequency selective power line channels in the presence of impulsive noise. Simulated results are also provided to further illustrate the superb performance of OFDM-IDMA in comparison with the traditional OFDMA system in terms of bit error rate (BER).