In this paper, we focus on designing energy-efficient power allocation schemes to improve the energy efficiency (EE) in multiuser multi-carrier two-way relay networks which are able to not only balance the EE of the two-way links but also ensure the quality-of-service (QoS). Specifically, the proposed design framework attempts to maximize a ratio of the spectral efficiency (SE) over the total network power consumption under a total power constraint as well as a signal-to-interference plus noise power ratio (SINR) constraint. The original problem is indeed non-convex, and we prove the convexity of the problem after a series of convex transformation. An iterative approach is proposed to find the local optimal solution of the original problem for achieving the maximum EE. Simulation results are provided to demonstrate the tradeoff between the EE and the SE.