In this present investigation, the authors obtain Fekete-Szegő’s inequality for certain normalized analytic functions \( f(z) \) defined on the open unit disk. As a special case of this result, Fekete-Szegő’s inequality for a class of functions defined through fractional derivatives is obtained. The motivation of this paper is to give a generalization of the Fekete-Szegő inequalities obtained by Srivastava and Mishra and Ma and Minda.