Abstract: The paper established the vertical dynamic governing equations of viscoelastic soil, where the stress-strain relationship of soil is described by fractional derivative viscoelastic model. Considering the three-dimensional wave effect of the soil-pile, the vertical vibration of soil described by fractional derivative viscoleastic model is solved by potential functions and the method of separation variables. The vertical coupled vibration of a pile in viscoleastic soil is investigated with boundary and contact conditions. The influences of mechanical parameters of pile and soil on the vertical vibration of a pile in viscoelastic soil are also analyzed. The results indicate that the order of fractional derivative, the model parameters of soil and the length-radius ratio have great impact on the complex stiffness and admittance at pile head; and the fractional derivative viscoelastic model can describe the mechanical behavior more accurately in larger range; and moreover, the influence of length-radius ratio becomes very smaller when the length-radius ratio increases to a certain value..