This paper presents a new cognitive radio network (CRN) framework with radio frequency (RF) energy harvesting, namely, RF-powered cognitive radio networks (RF-CRNs), wherein multiple secondary users (SUs) harvest energy from the RF signals of primary users (PUs) all the time except when transmitting data in the allocated time, namely, the “harvesting–transmission–harvesting” mode. In this way, the energy harvested by each SU can be maximized until the next data transmission. Also, the total energy consumed by the SUs must be less than or equal to the total harvested energy (the energy causality constraint), while the transmit power of SUs must be restricted to protect the PUs from interference (collision constraint). Finally, under the satisfaction of quality of service of SUs (throughput constraint), our goal is to determine the optimal transmitting time and power allocation that maximize the achievable throughput in the RF-CRNs. We achieved the optimal result by transforming the optimization problem into a convex optimization problem and then applying Lagrange multiplier methods. Extensive performance evaluations showed the efficiency of the proposed algorithm.