Cognitive Radio networks allow the unlicensed users to share the available spectrum opportunities. However, this demands for solving the problem of contention among multiple unlicensed user packets for transmission. In our paper, we consider the Opportunistic Spectrum Access model for packet transmission between two unlicensed users. We suggest a priority scheme for a unlicensed user to concurrently transmit different types of packets. Our scheme reserves a fixed number of queueing places in the buffer for the prioritized packets. We study the transmission performance under both the priority scheme and imperfect spectrum sensing, with respect to the blocking probabilities, average transmission delay and transmission throughput of unlicensed users packets. The Markov chain based numerical analysis is validated by simulation experiments. Our results show that the suggested priority scheme is able to enhance transmission throughput of unlicensed users packets, together with significant decreased average transmission delay and minor decreased total transmission throughput.