The problem of power allocation in maximizing the energy efficiency of the secondary user (SU) in a delay quality-of-service (QoS) constrained CR network is investigated in this paper. The average interference power constraint is used to protect the transmission of the primary user (SU). The energy efficiency is expressed as the ratio of the effective capacity to the total power consumption. By using non-linear fractional programming and convex optimization theory, we develop an energy efficiency power allocation scheme based on the Dinkelbach method and the Lagrange multiplier method. Numerical results show that the proposed scheme outperforms the existing schemes, in terms of energy efficiency.