Power line communication (PLC) utilizes power lines for the purpose of electronic data transmission. The performance of a PLC system is significantly affected by the additive and multiplicative power line noises; the additive noises are of two types, namely background noise and impulsive noise. Whereas, the multiplicative PLC noise leads to fading in the received signal strength. In this paper, we evaluate the performance of a PLC system over log-normal fading channel under Nakagami-m distributed additive background noise assuming binary phase shift keying modulation scheme. The analysis involving log-normal fading is very complicated. Hence we use a novel gamma approximation to log-normal distribution for our analysis. We evaluate the probability density function of the decision variable. A closed-form expression of the analytical average bit error rate of the considered system is derived. We also compute the diversity order of the considered PLC system. The validity of the derived analytical expressions is closely verified by the simulation results. © 2015 IEEE.