Abstract: This paper focuses on the energy-efficient power allocation in OFDMA systems. Different from the existing work, this paper proves that the optimal energy-efficient power allocation must have a special water-filling structure, named energy-efficient water-filling structure, by exploiting the strict pseudo-concavity of the energy efficiency function with respect to the power vector. Applying the energy-efficient water-filling structure, the original issue is simplified to a single-variable issue, and the closed-form optimal solution is further obtained. Based on the theoretical analysis, an optimal energy-efficient power allocation algorithm is proposed, where the optimal solution is achieved by sequentially searching within a finite number of water-level intervals. The simulation results demonstrate that the proposed algorithm achieves the optimal solution with significantly lower computational complexity compared with the conventional iterative methods.