Abstract: By using 3-ary differential functions, we construct an infinite dimensional 3-Lie algebra T, discuss the structure of T, and prove that T is a non-3-solvable non-simple 3-Lie algebra, the inner derivation algebra ad T is an indecomposable unsolvable Lie algebra, and the ideals of ad T have only the derived sequence V⁽ⁿ⁾ of the maximal ideal V(n∈Z, n≥0).

Key words: 3-Lie algebra, 3-solvable, inner derivation algebra