An extension of density functional theory is proposed for degenerate states. There are suitably selected basic variables beyond the subspace density. Generalized Kohn-Sham equations are derived. A direct method is proposed to ensure the fixed value of ensemble quantities. Then the Kohn-Sham equations are similar to the conventional Kohn-Sham equations. But the Kohn-Sham potential is different for different ensembles. A simple local expression is proposed for the correlation energy.