Cognitive　radio　(CR)　is　considered　as　one　of　the　most　promising　solutions　to　the　problem　of　overcrowded　spectrum　by　allowing　secondary　users　(SUs)　to　access　the　spectrum　dynamically.　Most　related　previous　work　on　CR　networks　with　primary　users＇　(PUs＇)　participation　ignores　the　SU　selection　scheme　when　the　spectrum　holes　cannot　satisfy　the　requirements　of　all　SUs.　In　this　paper,　we　propose　an　optimal　SU　selection　scheme　with　the　optimization　goals　of　maximizing　the　PU＇s　reward,　which　is　defined　as　the　summation　of　rent　collected　from　the　SUs.　To　solve　this　problem,　a　restless　bandit　approach　is　used,　which　dramatically　simplifies　the　computational　complexity.　Furthermore,　extensive　simulation　results　are　presented　to　show　the　significant　performance　improvement　of　the　proposed　scheme　compared　to　the　existing　ones.　©　2012　IEEE.