In　this　paper,　the　nonlinear　dynamical　characteristics　for　transverse　vibrations　of　axially　moving　viscoelastic　belt　were　investigated.　The　governing　equations　for　the　viscoelastic　moving　belt　were　derived　in　three-dimensional　space.　The　method　of　multiple　scales　and　the　Galerkin＇s　approach　were　applied　directly　to　the　partial　differential　governing　equation　of　motion　to　obtain　four-dimensional　averaged　equation.　The　results　of　numerical　simulation　demonstrate　that　there　exist　the　periodic　and　chaotic　motions　of　the　axially　moving　viscoelastic　belt.