In this paper we obtain a stability theorem of generalized Kähler
structures with one pure spinor under small deformations of generalized
complex structures. (This is analogous to the stability
theorem of Kähler manifolds by Kodaira-Spencer.) We apply the
stability theorem to a class of compact Kähler manifolds which
admits deformations to generalized complex manifolds and obtain
non-trivial generalized Kähler structures on Fano surfaces
and toric Kähler manifolds. In particular, we show that every
nonzero holomorphic Poisson structure on a Kähler manifold induces
deformations of non-trivial generalized Kähler structures.