In this paper, we study some equivalent conditions for a color hom-Lie algebra to be a complete color hom-Lie algebra. In particular, we discuss the relationship between decomposition and completness for a color hom-Lie algebra. Moreover, we check some conditions that the set of αs -derivations of a color hom-Lie algebra to be complete and simply complete. Finally, we find some conditions in which the decomposition into hom-ideals of the complete multiplicative color hom-Lie algebras is unique up to order of hom-algebra.