Cognitive orthogonal frequency-division multiplexing (OFDM) systems are spectrum-efficient yet vulnerable to intercarrier interference (ICI), especially in high-mobility scenarios. In this paper, the energy efficiency optimization problem in high-mobility cognitive OFDM system is considered. The aim is to maximize the energy efficiency by adapting subcarrier bandwidth, power allocation and sensing duration in the presence of ICI, under the constraints of the total power budget of secondary networks, the probabilistic interference limits for the protection of primary networks, and the subcarrier spacing restriction for high-mobility OFDM systems. In order to tackle the intractable non-convex optimization problem induced by ICI, an ICI-aware power allocation algorithm is proposed, by referring to noncooperative game theory. Moreover, a near-optimal subcarrier bandwidth search algorithm based on golden section methods is also presented to maximize the system energy efficiency. Simulation results show that the proposed algorithms can achieve a considerable energy efficiency improvement by up to 133% compared to the traditional static subcarrier bandwidth and power allocation schemes.