Nowadays, with the dramatically increased penetration of wireless access, the conflict between spectrum scarcity and under-utilisation is becoming more and more aggravating. A promising technology to tackle such challenge is cognitive radio, of which spectrum sensing is one of the most important functionalities. In this study, the authors consider an essential problem of energy-efficient spectrum sensing in cognitive radio networks. Although most existing works of spectrum sensing mainly focus on determining an optimal sensing time to maximise the detection probability and/or to minimise the false alarm probability, our problem of how to schedule the power-constrained sensor is much more challenging, because of the trade-off among interests of the primary user, secondary user and sensor. The authors formulate it as a non-linear optimisation problem to maximise the sensor lifetime, with necessary constraints of quality and delay of spectrum sensing, and throughput for performance guarantee of primary and secondary users. Moreover, the authors incorporate the distribution information of channel occupancy/vacancy durations into the problem to yield a desirable solution. They propose a novel framework to obtain the optimal energy-efficient periodic scheduling by adopting both non-linear programming and linear programming. Extensive simulation results are provided to validate our theoretical analysis.