In this paper, we investigate a two-way relaying power line communication (PLC) network with analog network coding. We focus on the analysis of the system outage probability, symbol error rate, and average capacity. Specifically, we first derive the probability density function (PDF) of the received signal-to-noise ratio (SNR) with a closed form, by exploiting the statistical properties of the PLC channel. Then with the help of this PDF, we develop the outage probability, symbol error rate, and average capacity with closed forms, based on the Hermite polynomial. Simulations show that the derived analytical results are consistent with those by Monte Carlo simulation.