Axial force exerted on an eccentric sphere by a focused Gaussian beam is studied within the framework of the generalized Lorenz-Mie theory (GLMT). The beam shape coefficients are calculated by integral localized approximation. The translational addition theorems for spherical vector wave functions and the boundary conditions are used in solving the scattering coefficients. Expression and numerical results of the radiation force for an eccentric sphere are given. By reducing the eccentric sphere to a concentric sphere system, the expression of axial force exerted on an eccentric sphere by a focused Gaussian beam is validated. The effects of distance between centers, beam waist, refractive-index and wavelength on axial radiation force are discussed.