Abstract: When investigating cognitive radio networks, in order to improve the energy efficiency of cognitive users with random access, we propose an energy efficient multiuser random access method which is based on the timevarying characteristic of channels. An energy consumption model for multiuser random access is set up. We use optimal stopping theory to analyze the maximum energy efficiency. It shows that the optimal scheduling scheme is a pure threshold policy, which can be obtained by adopting an iterative algorithm. We also investigate the tradeoff between energy efficiency maximization and throughput maximization. A sufficient condition is offered where energy efficiency and throughput can be maximized simultaneously. According to numerical results, it is found that when the transmission power is relatively large compared with contention power and probing power, we are able to maximize the throughput without an obvious degradation on energy efficiency. Furthermore, when users’ selfish behaviors are considered, we formulate a usercentric model, in which the loss of energy efficiency is less than 10% compared with networkcentric case when the number of users grows.