We study the Cauchy problem of a one-dimensional nonlinear viscoelastic model with fading memory. By introducing appropriate new variables we convert the integro-partial differential equations into a hyperbolic system of balance laws. When it is a perturbation of a constant state, the solution is shown time asymptotically approaching to predetermined diffusion waves. Pointwise estimates on the convergence details are obtained. © 2012 Wuhan Institute of Physics and Mathematics.