In this article, we investigate optimal beamforming at a multiantenna primary base station (PBS) and a multiantenna cognitive base station (CBS) for energy-efficient (EE) secure downlink communication in cognitive radio networks with one single-antenna primary user (PU), one single-antenna cognitive user (CU), and multiple single-antenna eavesdropping nodes. An artificial noise transmission scheme is used by CBS to protect the data against the eavesdropping security attacks at the cost of extra power consumption. To improve the secrecy energy efficiency (SEE), we propose a SEE maximization (SEEM) scheme by exploiting the instantaneous channel state information (CSI) of the eavesdroppers under the secrecy rate (SR) constraints of the PBS-PU and CBS-CU channels, the quality-of-service requirement of the PU, and the transmit power constraint of the CBS. When the eavesdropping links' instantaneous CSI are unknown at the legitimate transmitters (i.e., PBS and CBS), we propose another SEEM scheme based on the statistical CSI of the eavesdropping links. Since the formulated optimization problems with fractional objective functions are nonconvex and mathematically intractable, we first transform them into equivalent subtractive problems, and then, employ the difference of two-convex functions approximation method to arrive at approximate convex problems. In addition, new two-tier optimal BF algorithms are proposed. Finally, simulation results are presented to illustrate the effectiveness and performance gains of our proposed SEEM schemes over conventional SR-only maximization and EE-only maximization schemes.