In　this　paper,　the　stability　and　nonlinear　vibration　of　an　axially　moving　isotropic　beam　with　simply　supported　boundary　conditions　are　investigated.　The　equation　of　motion　of　the　axially　moving　beam　is　established　using　the　assumed　mode　method　and　Hamilton＇s　principle.　For　the　linear　system,　the　natural　frequencies　of　the　beam　under　different　moving　velocities　are　calculated　by　solving　the　generalized　eigenvalue　problem　of　the　system　to　analyze　the　divergence　and　flutter　velocities.　For　the　nonlinear　system,　the　bifurcation　of　the　transverse　displacement　with　respect　to　the　moving　velocity　is　analyzed　and　the　vibration　properties　of　the　beam　under　harmonic　excitation　are　presented.　From　the　investigation,　it　can　be　seen　that　with　the　moving　velocity　increasing,　the　beam　exhibits　the　divergence　or　the　flutter　types　of　instability.　The　beam　may　exhibit　a　transient　stable　state　before　flutter.　The　first　order　divergence　velocity　of　the　beam　obtained　from　the　linear　analysis　is　accordance　with　the　bifurcation　velocity　obtained　from　the　nonlinear　system.　The　nonlinear　forced　vibrations　of　the　beam　under　different　moving　velocity　are　presented　to　show　the　effects　of　the　moving　velocity　on　the　response　amplitude.　The　existence　of　the　transient　stable　state　is　also　proved　from　the　nonlinear　forced　vibration　analysis.