Abstract: A generalized functional Φ_{S, F} associated to maps between Riemannian manifolds is mainly studied. The first variation formula and the second variation formula of Φ_{S, F} are derived.By using the second variation formula, the stability of Φ_{S, F}-harmonic map is studied and the stability results of Φ_{S, F}-harmonic maps from sphere S^m(m≥5) or into sphere Sⁿ(n≥5) are obtained.