In this paper, we study the complete ⋆-metric semigroups and groups Raǐkov completion of invariant groups. We obtain following. (1) Let (X,d⋆) be a space containing semigroup (group) G that is dense subset X. If restriction d⋆ on invariant, then X can become as subgroup, (2) (G,d⋆) group such G. Then, if only (G,τd⋆) complete.