In this paper, we study the stability of flat fake domain walls solution of fake N = 1 supergravity in d + 1 dimensions with Kahler surface as the sigma model. We start with Lagrangian for N = 1 fake supergravity which is coupling between gravity and complex scalar in d + 1 dimensions with scalar potential turned on. Then, as in supergravity theory, we demand that the scalar fields span the Kahler manifold. The equations of motion for fields can be reduced into first order equations by defining the superpotential and the resulting equations are called the projection equation and the fake BPS equation. Finally, we discuss about the stability of flat fake domain walls by investigating the critical points of the superpotential and the scalar potential.