Abstract In this paper, we consider a scenario where the source node powered by the conventional power grid transmits data with the assistance of some energy harvesting (EH) decode-and-forward (DF) relay nodes. Unlike EH providing renewable energy, most power grids are supported by the non-renewable fossil fuels. So our goal is to maximize the non-renewable energy efficiency (EE) of the non-EH source throughout multiple timeslots. To deal with the randomness of energy arrivals and non-ideal circuit power, we formulate the EE optimization problem of the relaying system by combining the power allocation and the sleep mode in both the source and the relay. We firstly deal with this problem in a special case with just one timeslot and then solve it in a multi-timeslot scenario with dynamic programming (DP) approach. We also propose a heuristic algorithm with a complexity lower than the DP algorithm. We compare the performance of the two algorithms with a baseline scheme. Simulation results show that the heuristic algorithm provides close EE with the DP algorithm, and a significant EE gain over the baseline scheme.