In this paper a research is carried out into an RF energy harvesting-based cognitive radio network (RF EH-CRN), aimming at the maximization of energy efficiency of secondary user networks by jointly optimizing transmission time and transmission power. The secondary transmitter (ST) first harvests energy from the radio frequency (RF) signals of primary user (PU) and then communicates with SU. Besides, ST maintains possible remaining energy from previous transmission blocks as initial energy. To ensure the quality of service (QoS) of secondary network, we impose a minimum throughput requirement constraint on ST in the process of energy offciency (EE) maximization. As EE maximization is a nonlinear fractional programming problem, we propose a fast iteration algorithm based on Dinkelbach method to achieve optimal resource allocation. Simulation results demonstrate that with fast convergence speed this algorithm can significantly improve the EE of the system while guaranteeing QoS constraints.