Abstract: The existing resource allocation research for OFDMA relay networks investigate only frequency-domain allocation and power allocation with fixed time-domain allocation, which can not fit the user service changes in time-domain. An optimal energy-efficient resource allocation strategy and its simplified version are proposed for OFDMA relay network. A generalized model for resource allocation issue, which dynamically allocates time-domain, frequency-domain resources and power resources, is established. Due to the strong flexibility and adaptability, the model may apply to not only the fixed time-domain allocation system, but also the non-fixed time-domain allocation system. For non-full-buffer traffic, to ensure the users quality of service, an energy-efficiency maximization model is established for OFDMA non-cooperative relay networks by using the Lagrange multiplier algorithm to solve the issue. Taking into account the complexity of the algorithm, a simplified resource allocation strategy is proposed by using the Hungarian method. The theory and simulation results show that the optimal algorithm can get the energy-efficiency maximization, and the energy-efficiency difference between the simplified algorithm and the optimal algorithm is less than 5%, however, the complexity has been significantly reduced. Moreover, the dynamic time-domain allocation has more adaptive in uneven user distribution or link distribution than fixed time-domain allocation.