We present the calculation of phonon life time at low frequencies in an amorphous solid, which is assumed to be characterized by an elasticity that exhibits spatial fluctuation. Thermodynamic Green’s function method is used to compute phonon self-energy, and an iterative method is devised to obtain an improvement upon the first order perturbation calculation. The elasticity correlation is taken to be an exponentially falling function of distance. We obtain an inverse life time that varies as the fourth power of phonon frequency for small values of the latter, and whose frequency-dependence becomes weaker and weaker as the frequency increases.