Abstract: In the practical application of cognitive radio network, it is especially important to improve the energy efficiency for those energy-constrained cognitive users. This paper is from the point of view of maximizing the energy efficiency in the cognitive radio network and considers the case that the primary user’s signal which appears suddenly will bring the collision when the cognitive user is transmitting data. Then the single objective optimization problems which optimize the sensing time and the frame period separately and jointly are given. They are solved after the theoretical analyses which are also verified by the simulations. The results show that the energy efficiency firstly increases and then decreases with the increase of the sensing time as well as the frame period and there is a group of optimal sensing time and frame period to maximize the energy efficiency.