This　paper　presents　a　method　of　deriving　moment　invariants　under　similarity　transformation.　The　invariants　sets　are　algebraically　independent　and　complete.　The　method　can　be　adopted　for　arbitrary　dimension　and　order.　This　paper　also　presents　some　explicit　formulas　for　computing　invariant　sets＇　dimension,　which　reveals　how　the　number　of　invariants　increases　with　moments＇　order　and　dimension　elevating.　(C)　2015　Elsevier　Ltd.　All　rights　reserved.