With the rapid development of wireless network technologies and proliferation of related services such as multimedia applications, demands for wireless spectrum resources keep rising. Cognitive radio (CR) is a novel approach for better utilization of the scarce, already packed but highly underutilized radio spectrum. Meanwhile, exclusive functionalities such as spectrum sensing make energy efficiency (EE) a crucial issue in Cognitive Radios (CRs). In this paper, we focus on the energy-efficient power allocation for OFDM-based CRs with imperfect spectrum sensing. The EE maximization for secondary users (SUs) is formulated as a nonlinear fractional programming problem taking into account imperfect spectrum sensing such as miss detection and false alarm. Then by transforming the original problem into a parameter programming, the optimal power allocation is derived with the bisection search (BS) method and dual decomposition method (DDM). Simulation results illustrate the significant performance improvement of our scheme compared to an existing one with objective of maximizing system throughput rather than EE.