Abstract: The definitions of the metric Hom-3-Lie algebra and the metric multiplicative Hom-3-Lie algebra are introduced, and their basic structures are studied.It is proved that every metric Hom-3-Lie algebra can be decomposed into the direct sum of non-degenerate irreducible ideals which are irreducible metric Hom-3-Lie algebra.And metric Hom-3-Lie algebra and the metric multiplicative Hom-3-Lie algebra are constructed by the metric Hom-3-Lie algebras.

Key words: 3-Lie algebra, metric 3-Lie algebra, metric Hom-3-Lie algebra, metric multiplicative Hom-3-Lie algebra