We develop a dynamic spectrum access (DSA) strategy for cognitive radio networks where prioritized traffic is considered. Assume that there are three classes of traffic, one traffic class of the primary user and two traffic classes of the secondary users, namely, Class 1 and Class 2. The traffic of the primary user has the highest priority, i.e., the primary users can access the spectrum at any time with the largest bandwidth demand. Furthermore, Class 1 has higher access and handoff priority as well as larger bandwidth demand as compared to Class 2. To evaluate the performance of the proposed DSA, we model the state transitions for DSA as a multi-dimensional Markov chain with three-state variables which present the number of packets in the system of the primary users, the secondary Class 1, and secondary Class 2. In particular, the blocking probability and dropping probability of the two secondary traffic classes are assessed.