Herein, the authors consider harvested energy powered cognitive radio networks (CRNs) in which harvested energy is stored in a rechargeable battery which has finite capacity. In addition, a practical scenario in which the amount of harvested power is finite is taken into account. Cognitive users (CUs) opportunistically access a licensed channel (or primary channel); meanwhile, it should be ensured that their confidential communications are not leaked to an eavesdropper. We investigate an optimal spectrum sensing schedule and the optimal amount of transmission energy for the CUs in each processing time slot. In particular, at the beginning of each time slot, based on the remaining energy in the battery, CU transmitter decides either: 1) to be active to sense the channel and transmit its data if the channel is found vacant or 2) to stay inactive during the current time slot in order to save energy and wait for more incoming energy for use in the next time slots. The decision is based on expected secrecy transmission rate calculated for both cases over subsequent K time slots. The proposed scheme aims to improve long-term secrecy transmission rate of CRNs in comparison with a conventional scheme where the decision for the current time slot is made to maximize current secrecy transmission rate without considering any future reward.