Abstract: The constitutive relationship of soil aroud pile was described by fractional derivative viscoelastic model， and the pile-soil dynamic torsional interaction was modeled by equivalent torsional Winkler spring-damper，and the stiffness and damping coefficients of equivalent torsional Winkler spring-damper model of fractional derivative viscoelastic soil were obtained with the method of separation of variables． By considering the boundary conditions，the torsional complex stiffness at pile head was also got by the transfer matrix method． It was investigated the influence of model parameters of fractional derivative viscoelastic model and the parameters of pile and soil on the torsional complex stiffness at pile head by means of numerical example． The result indicated that the order of fractional derivative had a certain effect on torsional complex stiffness，while，the influence of embedded depth of the pile and the modulus ratio on torsional complex stiffness was great，and the influence of embedded depth of the pile on torsional complex stiffness has a certain relationship of the length of the exposed part of the pile． The effect of constitutive model parameters on the pile stiffness was more complex， the equivalent damping would be negative when the viscous terms of constitutive model was large．