In　the　real　life,　there　exist　many　complicated　game　situations　with　the　unequal　coalitions　and　more　than　one　relevant　or　irrelevant　objections.　First　of　all,　this　paper　constructs　the　multi-objective　cooperative　games　with　comprehensive　weights,　and　those　weights　are　associated　with　coalitions　and　objections.　Then　the　least　squares　prenucleolus　model　and　the　least　squares　nucleolus　model　of　the　multi-objective　cooperative　games　are　proposed　with　hybrid　objections,　including　the　irrelevant　objections　and　relevant　objections.　Second,　the　methods　of　least　squares　prenucleolus　and　the　algorithm　of　least　squares　nucleolus　in　the　classical　cooperative　games　are　extended　to　the　multi-objective　cooperative　games.　Using　Lagrange　multiplier　method　and　pseudo-inverse　theory,　we　have　the　explicit　expression　of　the　least　squares　prenucleolus　of　the　multi-objective　cooperative　games　and　an　algorithm　for　least　squares　nucleolus　of　the　multi-objective　cooperative　games,　and　also　prove　the　validity　of　the　algorithm　by　properties　of　convex　function.　Finally,　the　correctness　and　effectiveness　of　the　proposed　models　are　verified　though　an　numerical　example　of　water　resources　allocation,　and　the　advantages　of　the　proposed　models　are　reflected　by　comparison.　©　2020,　Editorial　Board　of　Journal　of　Systems　Engineering　Society　of　China.　All　right　reserved.