Opportunistic Spectrum Access (OSA) brings new research challenges in MAC protocol design. It allows unlicensed users to share licensed spectrum in space and time with no or little interference to Primary Users (PUs). When designing an OSA MAC protocol, one of the most difficult but important problem is how the unlicensed users decide when and which channel they should sense and access without conflicting the communications among PUs. To solve this problem, the unlicensed users should have the ability of adaptively and dynamically seeking and exploiting opportunities in both licensed and unlicensed spectrum and along both the time and the frequency dimensions. Secondary Users (SUs) as unlicensed users are required to sense radio frequency band, and when PU are detected, they must vacate the channel immediately within certain amount of time. Due to hardware and energy constraints, full spectrum availability cannot be sensed as well as they do not monitor when there is no data to be transmitted. In this paper, we study MAC protocol design for OSA in Cognitive Radio (CR) ad hoc network under Partially Observable Markov Decision Process (POMDP) algorithm that maximizes achievable throughput for SUs with sufficient protection to PUs. Furthermore, we study tractable greedy algorithm to reduce the complexity of POMDP calculation. The derivation of greedy approach proves that sensing problem can be solved either optimally or approximate the optimal solution. Computer simulation is used to evaluate the performances both of optimal and sub optimal strategy. ©2010 IEEE.