The　complex　natural　frequencies　for　linear　free　vibrations　and　bifurcation　and　chaos　for　forced　nonlinear　vibration　of　axially　moving　viscoelastic　plate　are　investigated　in　this　paper.　The　governing　partial　differential　equation　of　out-of-plane　motion　of　the　plate　is　derived　by　Newton＇s　second　law.　The　finite　difference　method　in　spatial　field　is　applied　to　the　differential　equation　to　study　the　instability　due　to　flutter　and　divergence.　The　finite　difference　method　in　both　spatial　and　temporal　field　is　used　in　the　analysis　of　a　nonlinear　partial　differential　equation　to　detect　bifurcations　and　chaos　of　a　nonlinear　forced　vibration　of　the　system.　Numerical　results　show　that,　with　the　increasing　axially　moving　speed,　the　increasing　excitation　amplitude,　and　the　decreasing　viscosity　coefficient,　the　equilibrium　loses　its　stability　and　bifurcates　into　periodic　motion,　and　then　the　periodic　motion　becomes　chaotic　motion　by　period-doubling　bifurcation.