In cognitive radio network (CRN), the secondary user (SU) opportunistically access the wireless channels whenever they are free from the licensed/primary user (PU). Even after occupying the channel, the SU has to sense the channel intermittently to detect reappearance of PU, so that it can stop its transmission and avoid interference to PU. Frequent channel sensing results in the degradation of SU's throughput whereas sparse sensing increases the interference experienced by the PU. Thus, optimal sensing interval policy plays a vital role in CRN. In the literature, optimal channel sensing strategy has been analyzed for the case when the ON-OFF time distributions of PU are exponential. However, the analysis of recent spectrum measurement traces reveals that PU exhibits heavy-tailed idle times which can be approximated well with hyper-exponential distribution (HED). In this paper, we deduce the structure of optimal sensing interval policy for channels with HED OFF times through Markov decision process. We then use dynamic programming framework to derive suboptimal sensing interval policies. A new multishot sensing interval policy is proposed and it is compared with existing policies for its performance in terms of number of channel sensing and interference to PU. © 2017 IEEE.