In this paper, a multiuser optimal stopping strategy for Opportunistic Spectrum Access (OSA) is proposed. In practical cognitive radio networks (CRNs), secondary users (SUs) usually have their own priorities of spectrum occupation, that is, SU with higher priority has a better chance to access idle channels in the spectrum. Since all SUs share the same spectrum information, throughput of the SUs with low priorities will be quite low even null if idle channels are always allocated to the SUs with high priorities. In another aspect, even if the SUs with low priorities also have chance to access idle channels, collisions will happen because of the competition among SUs. In order to increase system throughput of all SUs and avoid such collisions, we formulate this problem as an optimal stopping problem and propose an effective priority scheme with spectrum partition. In view of users' priorities, spectrum is partitioned completely into several channel sets, the amount of which equals to that of SUs. Thus, the problem can be simplified into multiple single-user cases. In each slot, each SU utilizes optimal stopping rule to determine which channel to access in consideration of channel states and exploration overhead. Simulation results show the effectiveness of the proposed strategy.