Green energy powered cognitive radio is proposed as a promising method to improve the energy efficiency (EE) and spectrum efficiency (SE). We consider the green power farms that harvest energy from solar and wind, which is used for the primary transmitter and the cognitive sensor network (CSN). The primary transmitter has priority to utilize the spectrum and the energy, and then the energy powered for the CSN may not be sufficient. Both the energy management and energy harvesting process will affect the throughput of the cognitive sensors (CSs). In this paper, we aim to design the system parameters in the CSN (including the sensing threshold, the sensing time, the final decision threshold in the fusion center, and the number of cooperating CSs) that can improve the utilization efficiency of the harvested energy and maximize the CSs’ throughput. Since the parameters are intertwined with the energy causality constraint and the average throughput, we decouple the influence of final decision threshold on the throughput from the influence of the sensing time and sensing threshold. The optimization problem is divided into two sub-problems. Algorithm 1 and Algorithm 2 are proposed to solve sub-problem 1 and sub-problem 2, respectively. The simulation results show that the proposed scheme can improve the average throughput significantly, and is able to achieve the best tradeoff between SE and EE.