The stress-strain relationship of soil is described by fractional derivative viscoelastic model, and established the vertical governing equations of viscoelastic soil. The stiffness and damping of the soil layer described by fractional viscoelastic model are obtained based on the method of layer. The pile-soil dynamic interaction is modeled by Winkler dynamic elastic-damping model, the pile to pile dynamic interaction and vertical vibration of the pile groups in the soil described by fractional derivative viscoelastic model is solved. The influence of the pile spacing, order of fractional derivative and model parameter of soil on the vertical dynamic impedance of pile groups is also investigated. The result indicated that the curves of the dynamic impedance varying with frequency were more complex with the increase of pile spacing, the influence of the order of fractional derivative on vertical dynamic impedance of pile groups is different at lower frequency and high frequency, and the selection of the constitutive model of viscoelastic soil had great effect on the vertical dynamic impedance of pile groups.