Nonlinear parametric vibration of a rotating viscoelastic beam with variable cross-section is studied. Nonlinear governing equation of the rotating viscoelastic beam with variable cross-section involving geometric nonlinearity is established based on Kelvin-Voigt constitutive relation. The governing equation is then transformed into an ordinary differential equation by using Galerkin method. Amplitude-frequency response is obtained by adopting the method of multiple scale. Finally, the influences of rotating velocityand radius of the hub on nature frequency and amplitude-frequency response are numerically discussed. It is shown that the unstable region increases with the increasing rotating velocity and radius of hub, but decreases with the increasing taper of the beam.