Energy efficient designs of communication systems are receiving great attention in both academia and industry. This letter investigates the energy efficient resource allocation schemes with Quality of Service (QoS) guarantee towards green wireless communication systems. We utilise the convex optimisation theory to obtain the optimal joint subcarrier and power allocation strategy. A new solution methodology is proposed to achieve the resolutions of transcendental equations. The simulation results demonstrate that our scheme outperforms other related approaches in terms of the energy efficiency performance, QoS guarantee and implementation complexity.