In　this　paper,　periodic　and　chaotic　oscillation　out　of　plane　are　investigated　for　viscoelastic　axially　moving　beam.　The　Kelvin　viscoelastic　model　is　chosen　to　describe　the　viscoelastic　property　of　the　beam　material.　Firstly,　the　nonlinear　governing　equations　of　out-of-plane　motion　are　established　by　using　the　Hamilton＇s　principle.　Then,　based　on　three-term　Galerkin＇s　discretization,　the　governing　equations　of　motion　are　simplified　to　ordinary　differential　equations　with　six-degrees-of-freedom.　The　bifurcation　diagram　and　phase　portraits　are　given　to　capture　the　system＇s　dynamical　behavior.　From　numerical　simulations,　it　is　indicated　that　the　periodic,　quasi-periodic　and　chaotic　motions　occur　in　the　out-of-plane　vibrations　of　the　axially　accelerating　viscoelastic　beam.