In a cognitive radio network, the full-spectrum is usually divided into multiple channels. However, due to the hardware and energy constraints, a cognitive user (also called secondary user) may not be able to sense two or more channels simultaneously. As different channels may have different primary user activities and time-varying channel qualities, an important task is to select which channels to sense and access for a given time period so that the available spectrum left by the primary users can be fully utilized by the secondary user. In this paper, we propose an optimal sensing channel selection policy based on partially observable Markov decision process (POMDP). The proposed policy takes the time-varying channel state into consideration and intends to optimally exploit spectrum resources for the secondary user. In addition to selecting optimal channel to sense, we also derive the optimal sensing time which leads to maximized throughput of the secondary user.