As　part　of　an　Internet　of　Things　(IoT)　framework,　the　Smart　Grid　(SG)　relies　on　advanced　communication　technologies　for　efficient　energy　management　and　utilization.　Cognitive　Radio　(CR),　which　allows　Secondary　Users　(SUs)　to　opportunistically　access　and　use　the　spectrum　bands　owned　by　Primary　Users　(PUs),　is　regarded　as　the　key　technology　of　the　next-generation　wireless　communication.　With　the　assistance　of　CR　technology,　the　quality　of　communication　in　the　SG　could　be　improved.　In　this　paper,　based　on　a　hybrid　CR-enabled　SG　communication　network,　a　new　system　architecture　for　multiband-CR-enabled　SG　communication　is　proposed.　Then,　some　optimization　mathematical　models　are　also　proposed　to　jointly　find　the　optimal　sensing　time　and　the　optimal　power　allocation　strategy.　By　using　convex　optimization　techniques,　several　optimal　methods　are　proposed　to　maximize　the　data　rate　of　multiband-CR-enabled　SG　while　considering　the　minimum　detection　probabilities　to　the　active　PUs.　Finally,　simulations　are　presented　to　show　the　validity　of　the　proposed　methods.　©　2020　by　the　authors.　Licensee　MDPI,　Basel,　Switzerland.