In　the　consensus　reaching　process　(CRP),　the　asymmetric　trust　relationships　among　decision-makers　(DMs)　and　discrepancies　of　DMs’　opinions　may　exacerbate　the　intra-group　conflicts.　In　this　paper,　we　investigate　a　consensus-building　approach　based　on　minimum　conflicts　under　budget　constraint　to　alleviate　the　conflicts.　First,　a　conflict　measurement　method　based　on　opinion　similarity　and　the　degree　of　asymmetric　trust　is　presented　to　construct　the　conflict　network　among　DMs.　Then,　the　weights　of　DMs　are　obtained　by　analyzing　the　structure　of　the　conflict　network.　To　achieve　a　consensus,　a　minimum　conflict　consensus　model　with　budget　constraint　(MCCMBC)　is　built.　Considering　that　the　impact　of　acceptance　degree　of　recommendations　on　consensus　results,　we　further　develop　the　Ε-MCCMBC,　the　rejection-based　(RB)-MCCMBC,　and　the　divergent-based　(DB)-MCCMBC　to　handle　compromise　limit,　rejection,　and　divergent　behaviors,　respectively.　Furthermore,　three　kinds　of　minimum　cost　budget　models　are　constructed　to　provide　the　reference　budget　of　CRP.　Finally,　the　validity　of　the　proposed　consensus　models　is　verified　by　the　case　of　trans-boundary　water　pollution　treatments　in　China＇s　Poyang　Lake　Basin.　The　results　show　that:　under　the　optimal　budget,　the　group　conflict　degree　and　the　collective　opinion　derived　from　the　MCCMBC　lie　somewhere　between　that　of　the　RB-MCCMBC　and　DB-MCCMBC.　In　addition,　the　moderator　needs　to　spend　more　budget　to　facilitate　the　CRP　when　DMs　adopt　rejection　or　compromise　limit　behaviors.　©　2022　Elsevier　Ltd