Energy efficiency and privacy preserving have become essential for the wireless sensor networks. In this paper, a joint energy and time resource allocation problem for the cognitive users (CUs) in a non-selfish symbiotic cognitive relaying scheme (NSCRS) is considered. We aim to maximize the total energy efficiency (EE) of the primary user and cognitive users with the consideration of information privacy under the total energy constraints of cognitive users. With full channel state information (CSI), an optimal energy and time resource allocation algorithm is proposed based on the exhaustive searching. Besides, in order to reduce the overhead of CSI feedback, a suboptimal algorithm, in which only the partial instantaneous CSI is required, is additionally proposed. Simulation results demonstrate the energy efficiency of primary and cognitive users in the NSCRS with consideration of information privacy can be greatly improved by the proposed algorithms.