Qualitative aspects of parametric excitation due to the non-constant traveling velocity of a viscoelastic string are investigated. The problem considered is an initially stressed viscoelastic string subjected to steady-state and harmonic variation of axially traveling motion. The string material is considered as a Violet element in series with a spring (three-parameter model). The partial differential equation of motion is derived first, and then is reduced to be a set of third-order nonlinear ordinary differential equations by applying Galerkin's method. Finally, the effects of elastic and viscoelastic parameters, constant and non-uniform transport speed, wave propagation speed ratio, and nonlinear terms on the transient amplitudes are investigated numerically.