In the framework of the general Lorenz-Mie theory, the scattering of an on-axis incident zero-order Bessel beam by an eccentric sphere is investigated. The electric and magnetic fields in different regions are expanded in terms of the sphere vector wave functions. Utilizing the boundary conditions of electromagnetic field, the expressions of expansion coefficient equations are given. Numerical simulations about the effect of Bessel beam half- angle, eccentricity, refractive index of inner sphere, radius of inner sphere on scattering are analyzed in detail.