Interference alignment (IA) is a promising technique for interference management and can be applied to spectrum sharing in cognitive radio (CR) networks. However, the sum rate may fall short of the theoretical maximum, particularly at low signal-to-noise ratio (SNR), and the quality of service (QoS) of the primary user (PU) may not be guaranteed. In addition, power allocation (PA) in IA-based CR networks is largely ignored, which can further improve its performance. Thus, in this paper, PA in IA-based CR networks is studied.