This study presents a newly developed technique for obtaining the theoretical scattering characteristics of the Luneberg lens. Generally, such calculations are approximated by using multi-layered, concentric sphere models. Here the Fredholm Integral Method (FIM) has been applied to the scattering problem, involving a single inhomogeneous sphere, where the refractive index of the sphere varies with radial distance from its centre. Comparisons are presented between scattering from the Luneberg lens, modeled by 3-, 5- and 10-layered spheres and by the FIM technique, for k0a values in the range 1.0 to 5.0. A comparison is also given, at k0a = 5.0 , with a differential equation solution.