Based on the theory of the scattering of an eccentric sphere arbitrarily illuminated by a shaped beam which is recently presented by us, and according to generalized Lorenz-Mie theory （GLMT）, we derived the series expressions of radiation forces exerted by the incident beam on an eccentric sphere by using the conservation law of electromagnetic momentum and the Mexwell-Tensor. As an example, numerical results of radiation force of absorbing eccentric spheres for off-axis incidence of Gaussian beam are given, along with a discussion about the influence of the beam-waist radius, relative complex refractive index, relative size and location of the inclusion on the forces.