Abstract: 13 classes of homogeneous Rota-Baxter 3-Lie algebras A_k are constructed by using the homogeneous Rota-Baxter operators R_k, 1≤k≤13, with weight 1 and satisfying g(0)+g(1)+1=0 on infinite dimensional simple 3-Lie algebra A_ω. It is proved that there are 5 classes of non-isomorphic homogeneous Rota-Baxter 3-Lie algebras D_i,1≤i≤5, in the homogeneous Rota-Baxter 3-Lie Algebra A_k,1≤k≤13, and the structure of each class of 3-Lie algebras D_i, 1≤i≤5, is studied.

Key words: 3-Lie algebra, Rota-Baxter operator, homogenous Rota-Baxter 3-Lie algebra