The so-called ding-a-ling model was first introduced by Dawson[1]and Casati independently introduced a modified version[2] which has an finite thermal conductivity κ.Subsequently,a one-dimensional system of particles which is a momentum conserving modification[3] of the famous “ding-a-ling” model has been confirmed to have an finite thermal conductivity κ independent of system length L,for L sufficiently large.In this paper,we investigate energy diffusion in momentum conserving one-dimensional lattice ding-a-ling model by measuring the correlation functions[4][5] of energy-momentum fluctuations at different times.