In a cognitive radio network (CRN), when the secondary users (SUs) are battery-powered devices, the concept of energy-efficient design is very important. In this paper, we propose an energy utility function by formulating the achievable data rate of a cooperative CRN in terms of the energy consumption by the CRN. The maximization of the energy utility function is obtained by jointly designing the sensing time, sensing threshold and number of cooperative SUs with the constraint of sufficient protect for primary users (PUs). Numerical results show that the CRN can achieve almost the maximum achievable data rate with significant energy saving.