In Cognitive Radio network, spectrum selection scheme is one of a important part to manage idle spectrums efficiently. However, in CR networks, they have to adopt time-varying channel availability to minimize the interference to primary users (PU), and be able to manage spectrum resources efficiently. In this paper, we proposed a modified PF scheduler which can be appropriate to schedule downlink CR users and channels, by considering the fairness and the throughput as well as the primary user characteristics of each channel.