The main purpose of the cognitive radio networks is considered to improve the spectrum efficiency by also taking into account the quality of the user experience. In this paper, we present a kind of partially observable priority queue model to capture the opportunistic spectrum access mechanism by focusing on the problems of the impatience for secondary user (SU) packets queueing in the buffer and the imperfect sensing results. Then, we construct transition probability matrix to analyze the stationary probability distribution of the spectrum access mechanism and derive the expressions for the throughput and the average delay of SU packets by taking into account the channel state and the imperfect sensing results. With numerical experiments, we reveal the trade-off between different performance measures.