In this study, wireless-powered cognitive radio networks (WPCRNs) are considered, in which N sets of transmitters, receivers and energy-harvesting (EH) nodes in secondary networks share the same spectrum with primary users (PUs) and none of the EH nodes is allowed to decode information but can harvest energy from the signals. Given that the EH nodes are untrusted nodes from the point of view of information transfer, the eavesdropping of secret information can occur if they decide to eavesdrop on information instead of harvesting energy from the signals transmitted by secondary users (SUs). For secure communications in WPCRNs, we aim to find the optimal transmit powers of SUs that maximize the average secrecy rate of SUs while maintaining the interference to PUs below an allowable level, while guaranteeing the minimum EH requirement for each EH node. First, we derive an analytical expression for the transmit power via dual decomposition and propose a suboptimal transmit power control algorithm, which is implemented in an iterative manner with low complexity. The simulation results confirm that the proposed scheme outperforms the conventional distributed schemes by more than 10% in terms of the average secrecy rate and outage probability and can also considerably reduce the computation time compared with the optimal scheme.