In this paper, secure communication for RF-powered cognitive networks has been investigated in which the secondary source (SS) transmits confidential information to the destination (SD) using the harvested energy form primary transmitter (PT) in the presence of a passive eavesdropper (SE). Note that the transmission power at the SS is subject to two important constraint: 1) the maximum transmission power at the SS determined by the harvested energy, 2) the peak interference power permitted at the primary receiver (PR). In order to obtain practical design insights into the reliability and security performance, we derive expressions of the connection outage probability, the secrecy outage probability, the transmission outage probability. We also derive the secrecy throughput i.e., the achievable secrecy rate at which the confidential messages are reliably and securely transmitted from the SS to the SD, to evaluate the overall performance of the RF-powered cognitive network. The numerical results provides insights into the effect of various system parameters, such as time splitting factor, transmitter power of primary user and the peak interference power threshold.