Equations describing circular Gaussian beams (CGB) propagating inside the absorptive Keer medium have been derived from nonlinear paraxial equation. Based on these equations, an evolution equation of the beam waist has been obtained. The evolution equation indicates that, depending on the beam and material parameters, the circular Gaussian beams may be convergent or divergent when travelling inside the nonlinear medium. There is a special threshold beam whose waist approaches zero at the point where the self focusing can just compensate for the diffraction. After solving the evolution equation, the threshold intensity and threshold focal length of the threshold beam have also been specified.