A Radio Frequency(RF) energy harvesting based Cognitive Radio Network(CRN) is proposed, where a Secondary User(SU) first harvests energy from the RF signals of Primary User(PU) and then transmits data using the harvested energy in one slot. The total consumed energy by the SU must be no more than the total harvested energy, in order to protect the PU from interference. Under the satisfaction of Quality-of-Service(QoS) of SU, the goal is to determine the optimal transmitting time and power allocation that maximizes its Energy Efficiency(EE) in the RF Energy Harvesting CRN(EH-CRN). In the process of maximizing energy efficiency, a balance is found between QoS and energy consumption. Less energy consumption allows the cognitive energy harvesting system to run more steadily and continuously, which is important while throughput constraint ensures the QoS of the system. To solve EE optimization as a nonlinear fractional optimization problem, it is firstly decomposed into two sub-problems by using Coordinate Ascendant, and then the nonconvex problem is transformed into an equivalent concave problem by using Charnes-Cooper Transformation method. Simulation results show the proposed scheme achieves effective EE.