Due　to　the　dramatic　increase　of　energy　consumption　in　wireless　communication　applications,　energy-efficient　networking　solutions　have　drawn　growing　attentions.　In　this　paper,　we　concentrate　on　the　design　of　an　energy-efficient　sensing　and　transmission　strategy　for　a　secondary　user　(SU)　in　a　cognitive　radio　network.　We　consider　the　scenario　that　multiple　heterogeneous　licensed　channels　exist,　and　the　SU　senses　channels　according　to　a　sequence　before　it　decides　to　access　or　to　sleep.　Energy　is　consumed　in　sensing,　transmission　and　operating.　We　model　the　occupancy　activities　of　primary　users　as　a　Markov　process,　and　formulate　the　problem　of　dynamically　sensing,　transmission　or　sleep　as　a　partially　observable　Markov　decision　process.　To　solve　the　problem,　we　discuss　the　myopic　policy　which　merely　focuses　on　the　energy　efficiency　over　a　frame.　By　exploring　a　parametric　problem,　we　establish　the　optimal　threshold　structure　of　the　strategy,　according　to　which　the　SU　decides　the　sensing　order,　as　well　as　when　and　which　channel　to　access.　Furthermore,　we　design　both　optimal　and　approximate　algorithms　accordingly.　Simulation　results　show　that　our　algorithms　can　effectively　increase　the　energy　efficiency　compared　with　the　full　sensing,　random　sensing　and　throughput　maximization　algorithms,　while　keep　limited　loss　of　throughput.