This paper presents a selective spectrum sensing and access strategy in a cognitive radio sensor network (CRSN), in order to maximize the throughput of secondary user (SU) system. An SU senses multiple channels simultaneously via wideband spectrum sensing. To maximize the throughput and reduce the sensing energy consumption, not all of the channels are sensed. The SU selects some channels for spectrum sensing and accesses these channels based on the sensing results. The unselected channels are accessed directly with low transmission power. A selection making algorithm based on partially observable Markov decision process (POMDP) theory is proposed, to make the SU determine which channels are selected for sensing, how long the sensing time, and the transmission powers of channels. An optimal policy and a myopic policy are proposed to solve the proposed POMDP problem. Moreover, an optimization problem is proposed to solve the synchronism problem among the selected channels. Numerical results show that the proposed selective spectrum sensing and access strategy improves the system performance efficiently.