There　are　a　lot　of　multi-objective　optimization　problems　(MOPs)　in　the　real　world,　and　many　multi-objective　evolutionary　algorithms　(MOEAs)　have　been　presented　to　solve　MOPs.　However,　obtaining　non-dominated　solutions　that　trade　off　convergence　and　diversity　remains　a　major　challenge　for　a　MOEA.　To　solve　this　problem,　this　paper　designs　an　efficient　multi-objective　sine　cosine　algorithm　based　on　a　competitive　mechanism　(CMOSCA).　In　the　CMOSCA,　the　ranking　relies　on　non-dominated　sorting,　and　the　crowding　distance　rank　is　utilized　to　choose　the　outstanding　agents,　which　are　employed　to　guide　the　evolution　of　the　SCA.　Furthermore,　a　competitive　mechanism　stemming　from　the　shift-based　density　estimation　approach　is　adopted　to　devise　a　new　position　updating　operator　for　creating　offspring　agents.　In　each　competition,　two　agents　are　randomly　selected　from　the　outstanding　agents,　and　the　winner　of　the　competition　is　integrated　into　the　position　update　scheme　of　the　SCA.　The　performance　of　our　proposed　CMOSCA　was　first　verified　on　three　benchmark　suites　(i.e.,　DTLZ,　WFG,　and　ZDT)　with　diversity　characteristics　and　compared　with　several　MOEAs.　The　experimental　results　indicated　that　the　CMOSCA　can　obtain　a　Pareto-optimal　front　with　better　convergence　and　diversity.　Finally,　the　CMOSCA　was　applied　to　deal　with　several　engineering　design　problems　taken　from　the　literature,　and　the　statistical　results　demonstrated　that　the　CMOSCA　is　an　efficient　and　effective　approach　for　engineering　design　problems.