Owing to its high spectrum efficiency (SE), two-way relaying has aroused tremendous research interests. In this paper, the spectrum-energy efficiency (SE-EE) trade-off in decode-and-forward (DF) two-way multi-relay networks is studied by considering non-ideal power amplifiers and non-negligible circuit. Firstly, we consider the scenario of several relay nodes. To achieve better performance, the relay node with the highest energy efficiency (EE) is selected as the optimal one. Secondly, we design the optimal power allocation method to allocate each node with the optimal transmission power to enhance EE and SE. Finally, we evaluate the performance of our method and additionally analyze how the change of relay nodes' relative position influences the EE and SE. Simulation results show that: 1) the proposed method can achieve higher SE than optimal relay equal power allocation, random relay equal power allocation, and optimal power allocation only; 2) the proposed method can achieve higher EE than optimal relay equal power allocation, random relay equal power allocation, and optimal power allocation only; and 3) EE and SE increase at first and then decrease when relay nodes move from the middle of the source node and destination node to both ends.INDEX TERMS Decode-and-forward (DF), energy efficiency (EE), multi-relay, relay selection, spectrum efficiency (SE), two-way relay.