In this paper, we investigate the average waiting time of packets with different priorities in cognitive radio networks (CRN) using a preemptive priority queuing system. Specifically, we consider two scenarios for CRN, the first with the secondary user (SU) sensing at the beginning of each time slot and the other with the SU having continues sensing ability. Our analysis shows that the average waiting time of packets for the SU does not only depend on the size of packets and arrival rate of the SU traffic but also depends on the arrival rate and size of packets from primary users (PU). Moreover, the results show that an SU with continuous sensing ability can utilize spectrum better than sensing at the beginning of each time slot.