The paper studies invariant complex Dirac structures with constant real index. Recall that a Dirac structure on a manifold \(M\) is a subbundle \(L\subset TM\oplus T^*M\) which is both maximal isotropic with respect to the natural symmetric pairing defined on \(TM\oplus T^*M\) and involutive with respect to the Courant bracket. It is possible to extend the natural pairing and the Courant bracket, which leads to the notion of complex Dirac structures. In this paper, the authors first recall the relevant notions and results. They introduce the concept of flag manifolds and review generalized complex structures, which are a special case of complex Dirac structures. The authors then prove the main result, which is the classification of all invariant complex Dirac structures with constant real index on a maximal flag manifold under the action of B-transformations in terms of the roots of the Lie algebra which defines the flag manifold. Explicit examples of invariant complex Dirac structures for the maximal flag manifolds associated to the semisimple Lie algebras are also given.