In this paper, we address the problem of energy-efficient power allocation for secure communications in an amplify-and-forward (AF) large-scale multiple-input multiple-output (LS-MIMO) relaying system in presence of a passive eavesdropper. The benefits of an AF LS-MIMO relay are exploited to significantly improve the secrecy performance, especially the secrecy energy efficiency (bit per Joule). We first analyze the impact of transmit power at the relay on the secrecy outage capacity, and prove that the secrecy outage capacity is a concave function of transmit power under very practical assumptions, i.e. no eavesdropper channel state information (CSI) and imperfect legitimate CSI. Then, we propose an energy-efficient power allocation scheme to maximize the secrecy energy efficiency. Finally, simulation results validate the advantage of the proposed energy-efficient scheme compared to the capacity maximization scheme.