From the nonlinear Schrdinger equation of beam propagating in Kerr absorbing medium, a set of evolution equations describing Gaussian beam waist radius have bean deduced. As taking no account of high order expanded term, the evolution of beam waist radius in medium without or with absorption has bean analyzed theoretically. And the result is that the beams would form solitary wave only as inputting at waist, no absorption are acquired. As taking account of high order expanded terms, there exists no solitary wave in beam propagation by numerical analysis without or with absorption, and the beams are controlled by input intensity. When input intensity is smaller, the beam would behave self-focusing only. Along with the increasing of input intensity, there is a threshold. As the input intensity is below this threshold, the input beam behaves self-focusing still; but as the input intensity surpasses this threshold, the input beam behaves diffraction strongly, no self-focusing occurs at all.