In　the　consensus　reaching　process　(CRP),　decision-makers　(DMs)　often　present　behaviors　of　tolerance　and　limited　compromise　when　adjusting　their　opinions,　which　may　lead　to　the　actual　decision　deviating　from　the　solution　recommendation　obtained　by　applying　the　current　minimum　cost　consensus　theory.　In　this　paper,　we　propose　a　consensus-reaching　approach　based　on　maximum　satisfaction　under　budget　constraints　for　DMs　with　these　two　behaviors.　To　obtain　a　feasible　budget　constraint　of　the　CRP,　a　reference　budget　consensus　model　(RBCM)　incorporating　both　of　these　behaviors　is　first　developed.　Under　the　constraint　of　the　limited　budget,　we　propose　a　maximum　satisfaction　consensus　model　(MSCM)　to　maximize　the　satisfaction　level　of　all　DMs　based　on　the　goal　programming　theory.　To　further　achieve　different　levels　of　consensus,　we　propose　a　soft　MSCM　under　a　certain　threshold　using　soft　consensus　measures.　Moreover,　the　proposed　consensus　models　are　illustrated　by　the　data　of　China＇s　Taihu　Lake　pollution　control.　The　results　suggest　that:　First,　the　individual　tolerance　behavior　has　a　higher　impact　on　the　consensus　outcome　than　the　compromise　limit,　whereas　the　latter　is　more　likely　to　affect　the　satisfaction　of　each　DM.　Second,　as　the　budget　increases,　the　consensus　opinion　and　group　satisfaction　level　will　increase　toward　a　higher　average　cost　until　they　remain　constant.　Last,　a　higher　consensus　threshold　will　reduce　DMs’　satisfaction　levels,　and　an　appropriate　threshold　should　be　selected　as　the　control　baseline　of　the　CRP　in　the　real　application.　©　2021　Elsevier　B.V.