The nonlinear dynamic behavior of a dielectric elastomer (DE) tube considering the viscoelastic effect is investigated. By employing the springdashpot model and the neo-Hookean model of the incompressible soft materials, the governing equation is constructed for the viscoelastic DE tube. With the aid of the small disturbance method, the analytical expression of the instantaneous intrinsic frequency is obtained. The effect of the characteristic time, the prestretch and the thickness parameter on the instantaneous intrinsic frequency is studied. The nonlinear responses of the DE tube under the periodic voltage excitation are presented. It is shown that the amplitude of the response is greatly suppressed by the viscous effect, while the intrinsic frequency of the quasi-static state in the end is not affected by the viscous effect. Only the principal resonance is observed for the case that no DC voltage component is applied. The multiple frequency resonance phenomena are observed for the case that a large enough DC voltage component is applied.