In this study, the energy-efficiency (EE) problem is investigated for downlink Orthogonal Frequency Division Multiple Access (OFDMA) cellular networks. The EE maximization problem is defined under certain prescribed per-user quality-of-service (QoS) demands and maximum system power limit. EE metric that aims to maximize the system data rate and minimize the total power consumption at the same time is used as the objective function of the defined problem. In this form the optimization problem belongs to a broad class of problems called mixed-integer non-linear programming problem (MINLP), that is difficult to solve in its original form in such a multi-carrier, multiuser networks. Hence, we have decomposed the original problem into two parts and presented a solution that performs subchannel allocation and power allocation parts separately. Simulation results are obtained to confirm the performance of the presented scheme in terms of energy-efficiency and total data rate.