Spectrum　selection　is　crucial　in　improving　the　performance　of　cognitive　radio　networks.　Most　of　previous　work　on　spectrum　selection　consider　spectrum　utilization　ratio　as　system　design　criteria　and　ignore　the　energy　issue.　In　this　paper,　we　take　a　cross-layer　design　approach　to　select　the　optimal　spectrum　considering　the　time　varying　and　stochastic　nature　of　wireless　channels.　The　proposed　scheme　selects　one　spectrum　among　different　alternatives　and　sets　the　modulation　and　coding　scheme　and　frame　size　in　each　time　slot　according　to　the　channel　state,　which　is　modeled　as　finite-state　Markov　channel,　with　the　objective　of　minimizing　energy　consumption.　The　procedure　of　spectrum　access　is　formulated　as　a　restless　bandit　problem,　which　can　be　solved　using　linear　programming　(LP)　and　primal-dual　index　heuristic　algorithm.　Simulation　results　are　presented　to　show　the　performance　improvement　of　the　proposed　scheme.