The non-linear dynamic stability and chaotic motion of viscoelastic transmission belt with time-dependent velocities and subjected to a transverse distributed varying external excitation is investigated. Based on the constitutive description of Kelvin viscoelastic material and the motion equation of the axially moving belt, the nonlinear dynamic model that dominates the transverse vibration of the viscoelastic transmission belt is established. And then one mode approximation of the governing equation is obtained by the Galerkin's method. This approximation leads to a parametrically excited Duffing's oscillator which exhibits a symmetric pitchfork bifurcation as the axial velocity of the belt is varied beyond a critical value. Finally, Melnikov's criterion is employed to find out the parameter regime（such as steady velocity, fluctuation velocity, external force and material property etc） in which chaos occurs. It is found that:1) Chaos region is above a line in the first quadrant if both velocity and external fluctuation coexist. And chaos region become large with the increasing of frequency of external excitation, but chaos region become small with the increasing of frequency of velocity fluctuation. Meanwhile the line always passes a fixed point if the frequency of external excitation or velocity fluctuation is not change. At this time chaos can not be controlled by the adjustment of external force or speed magnitude. 2) For lower speed fluctuation frequencies, one can employ higher steady speeds and maintain the amplitude of speed fluctuations to avoid chaos, however, for higher speed fluctuation frequencies, one can only avoid chaos by decreasing the steady velocity of the belt. 3) Chaos region become small with the increasing of material viscosity, but chaos regions become large with the increasing of material stiffness.
