A green cognitive radio network (CRN), characterized by base stations (BSs) that conserve energy during sleep periods, is a promising candidate for realizing more efficient spectrum allocation. To improve the spectrum efficiency and achieve greener communication in wireless applications, we consider CRNs with an long term evolution advanced (LTE-A) structure and propose a novel energy-saving strategy. By establishing a type of preemptive priority queueing model with a single vacation, we capture the stochastic behavior of the proposed strategy. Using the method of matrix geometric solutions, we derive the performance measures in terms of the average latency of secondary user (SU) packets and the energy-saving degree of BSs. Furthermore, we provide numerical results to demonstrate the influence of the sleeping parameter on the system performance. Finally, we compare the Nash equilibrium behavior and social optimization behavior of the proposed strategy to present a pricing policy for SU packets.