We show that the recently proposed invariant eigenoperator method can be successfully applied to solving the energy levels of an electron in a saddle-potential quantum dot under a uniform magnetic field.The Landau diamagnetism decreases with the value ω y 2-ω x 2 due to the existence of the saddle potential. We show that the recently proposed invariant eigenoperator method can be successfully applied to solving the energy levels of an electron in a saddle-potential quantum dot under a uniform magnetic field. Landau diamagnetism decreases with the value ω y 2-ω x 2 due to the existence of the saddle potential.