Cognitive radio technology enables us to utilize the extra spectrum which is not used by the primary users by sensing the channel condition. To use such an extra spectrum, spectrum allocation is one of the important issues in the cognitive radio networks. The network is dynamic and the available channels are changeable, and the opportunistic channel allocation is required to use the resource efficiently without interference to the primary networks. In this paper, modified proportional fairness scheduling is proposed for cognitive radio networks to satisfy the both fairness and system throughput, and the modified scheduling was designed to reduce the interference to the primary users.