The　non-planar　transverse　nonlinear　vibrations　of　an　axially　accelerating　viscoelastic　belt　with　one-to-one　internal　resonance　are　investigated　for　the　first　time.　The　nonlinear　equations　of　motion　of　an　axially　accelerating　viscoelastic　belt　are　developed　using　the　generalized　Hamilton＇s　principle.　The　method　of　multiple　scales　and　the　Galerkin＇s　approach　are　applied　directly　to　the　partial　differential　governing　equations　of　motion　to　obtain　four-dimensional　averaged　equation　under　the　case　of　one-to-one　internal　resonance　and　primary　parametric　resonance　of　the　first　order　modes　for　the　in-plane　and　out-of-plane　vibrations.　Numerical　method　is　used　to　investigate　nonlinear　dynamics　characteristic　of　an　axially　accelerating　viscoelastic　belt.　The　results　of　numerical　simulation　show　that　there　exist　the　periodic　motion　and　the　chaotic　motion　of　an　axially　accelerating　viscoelastic　belt.