We report on the theory of a Luneburg lens for forward-volume magnetostatic spin waves and verify its operation via micromagnetic modelling. The lens converts a plane wave to a point source, and vice versa, by a designed graded refractive index, realized by modulating either the thickness or the saturation magnetization in a circular region. We find that the lens enhances the wave amplitude by about 5 times at the lens focus, and 47% of the incident energy arrives in the focal region. A lens with small deviations from the optimal profile can still result in good focusing if the index is graded smoothly.