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This paper deals with a class of nonlinear viscoelastic wave equation with damping and source terms utt-Δu-Δut-Δutt +∫t0 g(t-s)Δu(s)ds + ut|ut |m-2 =u|u|p-2 with acoustic boundary conditions.Under some appropriate assumption on relaxation function g and the initial data,we prove that the solution blows up in finite time if the positive initial energy satisfies a suitable condition.