A pseudo-Einstein contact form, which is a contact form satisfying a weak Einstein condition, is necessary for defining some global invariants for strictly pseudoconvex CR manifolds: for example, the total Q-prime curvature and the Burns-Epstein invariant. When we consider the variation of such an invariant, the question arises whether the existence of a pseudo-Einstein contact form is preserved under deformations of CR structures. In this talk, we will answer this question affirmatively for deformations as a real hypersurface in a fixed complex manifold.