Due　to　emerging　requirements　and　pressures　related　to　environmental　protection,　manufacturing　enterprises　have　expressed　growing　concern　for　adopting　various　energy-saving　strategies.　However,　environmental　criteria　were　usually　not　considered　in　traditional　production　scheduling　problems.　To　overcome　this　deficiency,　energy-saving　scheduling　has　drawn　more　and　more　attention　from　academic　scholars　and　industrial　practitioners.　In　this　paper,　an　energy-saving　flexible　job　shop　scheduling　problem　(EFJSP)　is　introduced　in　accordance　with　the　criterion　of　optimizing　power　consumption　and　processing　costs　simultaneously.　Since　the　classical　FJSP　is　strongly　NP-hard,　an　Improved　Sparrow　Search　Algorithm　(ISSA)　is　developed　for　efficiently　solving　the　EFJSP.　In　the　ISSA,　a　Hybrid　Search　(HS)　method　is　used　to　produce　an　initial　high-quality　population;　a　Quantum　Rotation　Gate　(QRG)　and　a　Sine-Cosine　Algorithm　(SCA)　are　integrated　to　intensify　the　ability　of　the　ISSA　to　coordinate　exploration　and　exploitation;　the　adaptive　adjustment　strategy　and　Variable　Neighborhood　Search　(VNS)　are　applied　to　strengthen　diversification　of　the　ISSA　to　move　away　from　local　optima.　Extensive　computational　experiments　validate　that　the　ISSA　outperforms　other　existing　algorithms　in　solving　the　EFJSP　due　to　the　advantages　of　intensification　and　diversification　mechanisms　in　the　ISSA.