Based on the theoretical researches on the scattering of an eccentric sphere arbitrarily illuminated by a shaped beam and the radiation force exerted by an off-axis incident Gaussian beam on the eccentric sphere, which are recently presented by us, the radiation force of the eccentric sphere acted by an arbitrarily incident Gaussian beam is calculated exactly and analysed in this paper. The series expressions of the radiation force of the eccentric sphere arbitrarily located in a Gaussian beam are provided. After the comparison with the results presented in the literature for the case of two-layered sphere, the radiation forces are numerically calculated when the inner core’s radius, distance between the two centers, incidence angles are different respectively. Considering the polarized direction of the beam, the relationship between the radiation force and the polarized direction of the beam for different incidence angle is analyzed too.