The　flexible　job　shop　scheduling　problem　(FJSP)　is　a　difficult　discrete　combinatorial　optimization　problem,　which　has　been　widely　studied　due　to　its　theoretical　and　practical　significance.　However,　previous　researchers　mostly　emphasized　on　the　production　efficiency　criteria　such　as　completion　time,　workload,　flow　time,　etc.　Recently,　with　considerations　of　sustainable　development,　low-carbon　scheduling　problems　have　received　more　and　more　attention.　In　this　paper,　a　low-carbon　FJSP　model　is　proposed　to　minimize　the　sum　of　completion　time　cost　and　energy　consumption　cost　in　the　workshop.　A　new　bio-inspired　metaheuristic　algorithm　called　discrete　whale　optimization　algorithm　(DWOA)　is　developed　to　solve　the　problem　efficiently.　In　the　proposed　DWOA,　an　innovative　encoding　mechanism　is　employed　to　represent　two　sub-problems:　Machine　assignment　and　job　sequencing.　Then,　a　hybrid　variable　neighborhood　search　method　is　adapted　to　generate　a　high　quality　and　diverse　population.　According　to　the　discrete　characteristics　of　the　problem,　the　modified　updating　approaches　based　on　the　crossover　operator　are　applied　to　replace　the　original　updating　method　in　the　exploration　and　exploitation　phase.　Simultaneously,　in　order　to　balance　the　ability　of　exploration　and　exploitation　in　the　process　of　evolution,　six　adjustment　curves　of　a　are　used　to　adjust　the　transition　between　exploration　and　exploitation　of　the　algorithm.　Finally,　some　well-known　benchmark　instances　are　tested　to　verify　the　effectiveness　of　the　proposed　algorithms　for　the　low-carbon　FJSP.