Relaying over power line communication (PLC) channels has the potential to improve the reliability and robustness of many PLC-based applications. In particular, this paper proposes to enhance the energy efficiency (EE) of a dual-hop relaying PLC system in the presence of impulsive noise by considering energy-harvesting (EH) at the relaying modem. Amplify-and-forward (AF) relaying and time-switching relaying EH protocols are deployed in this paper. The PLC modems are assumed to have the capability to go on low-power consumption sleep mode when they are neither transmitting nor receiving. The system performance is evaluated in terms of EE and average outage probability for which analytical expressions are derived. Using the derived expressions, several system parameters are investigated, such as the channel gain, which is related to the number of network branches, EH time factor and impulsive noise characteristics. Particularly, the optimization problem of the EH time is addressed thoroughly in order to maximize the achievable gains. Results reveal that the proposed system can offer considerable improvements compared with the conventional AF relaying scheme.