In this paper, we investigate a security mode decision policy for a cognitive radio network (CRN) powered by a non-radio frequency energy harvester. In such a network, a cognitive user (CU), which has a finite battery capacity, senses the presence of the primary user and tries to access the time-slotted primary channel opportunistically to transmit data. However, communication can be vulnerable to sudden attacks that are carried out by hidden eavesdroppers. Therefore, we propose an energy-efficient data encryption scheme for CRNs to increase the effective security level under energy limitation constraints. The operation mode decision policy is formulated as a framework of a partially observable Markov decision process. In this approach, based on the sensing results and the remaining energy at the beginning of each time slot, CUs can decide to stay silent to save energy, or become active and encrypt data using opportune private-key encryption methods considering the effect of the current action on the future reward to maximize the effective security. Finally, we evaluate the performance of the proposed scheme by using numerical simulation results.