Energy-efficient resource allocation is considered for cognitive cooperative radio networks (CCRNs) with imperfect spectrum sensing. The optimization problem of maximizing energy efficiency (EE) is formulated over the transmission power and sensing time subject to some practical limitations, such as the individual power constraint for secondary source and relay, the quality of service (QoS) for the secondary system, and effective protection for the primary user (PU). Given the complexity of this problem, two simplified versions (i.e., perfect and imperfect sensing cases) are studied in this paper. We transform the considered problem in fractional form into an equivalent optimization problem in subtractive form. Then, for perfect sensing, the Lagrange dual decomposition and iterative algorithm are applied to acquire the optimal power allocation policy; for imperfect sensing, an exhaustive search and iterative algorithm are proposed to obtain the optimal sensing time and corresponding power allocation. Finally, numerical results show that the EE design greatly improves EE compared with the conventional spectrum-efficient design.