Energy efficiency (EE) is critical to achieve cooperative sensing and transmission in relay-assisted cognitive radio networks (CRNs) with limited battery capacity. This paper proposes an energy-efficient cooperative transmission strategy with combined censoring report and spatial diversity in cooperative process, namely, censoring-based relay transmission (CRT). Specifically, secondary relays (SRs) take part in cooperative sensing with differential censoring to reduce energy consumption, and the best SR assists secondary transmission to enhance communication quality in transmission stage and thus to improve secondary transmission EE. First, we derived generalized-form expressions for detection probability, reporting probability, sensing energy, and expected throughput for CRT. Second, we investigate a mean EE-oriented maximization nonconvex problem by joint optimizing sensing duration and power allocation for secondary users under secondary outage probability and sensing performance constraints. With the aid of Jensen’s inequality, an efficient cross-iteration algorithm with low complexity is proposed to obtain the suboptimal solutions, which is developed by golden segmentation search method. Finally, extensive simulations are conducted to evaluate the performance of CRT. The results show significant improvements of SUs’ EE compared with traditional noncooperation single cognitive transmission schemes, which demonstrate the benefits of our proposed cooperative strategy in conserving energy for secondary transmission.