In this paper, we focus on a green energy-powered allocations for OFDM-based Cognitive Radio (CR) networks composed of the secondary users (SUs) and the primary users (PUs). We analyse a green energy-efficient (EE) power allocation problem at the SU level under feasibility constraints. When the SU is allowed to transmit, these constraints guarantee a minimum SU's Quality of Service (QoS) level, a maximum average transmit power and the protection of the PUs. The green energy-powered allocation problem under study is the weighted difference between overall achievable rate and power consumption. Since the opposing character of the constraints, it is difficult to solve this green energy-powered allocation problem via conventional optimization tools. Therefore, we propose an efficient iterative water-filling algorithm in order to find the optimal power allocation.