Let H ⊂G be real reductive Lie groups. A discrete series representation for a homogeneous space G/H is an irreducible representation of G realized as a closed G-invariant subspace of L²(G/H). The condition for the existence of discrete series representations for G/H was not known in general except for reductive symmetric spaces. This paper offers a sufficient condition for the existence of discrete series representations for G/H in the setting that G/H is a homogeneous submanifold of a symmetric space \tilde{G}/\tilde{H} where G ⊂\tilde{G} ⊃\tilde{H}. We prove that discrete series representa-tions are non-empty for a number of non-symmetric homogeneous spaces such as Sp(2n,R)/Sp(n₀,C)×GL(n₁,C)×...×GL(n_k,C) (n_j=n) and O(4m,n)/U(2m,j) (0≤2j≤n).