To investigate the vertical vibration characteristic of a large-diameter floating pile，a threedimensional fictitious soil pile model（TFSP）is presented by introducing a three-dimensional visco-elastic con? tinuum theory and considering the three-dimensional wave propagation effect of the pile and pile end soil. First，the fundamental solutions of pile shaft and fictitious soil pile are derived by using Laplace transform and variables sepa? ration methods. Then，combining the compatibility conditions at the interfaces of pile-soil and pile-TFSP，the ana? lytical solution of dynamic impedance at the head of a large-diameter pile is obtained. The rationality and accuracy of the proposed model and corresponding analytical solutions are verified by comparing them with existing research.Finally，the numerical examples are performed to investigate the effect of the radial location of the pile cross-section and parameters of TFSP on the dynamic impedance of a large-diameter floating pile. The results indicate that the dy? namic stiffness and damping of the pile head decrease from the pile center to the pile edge，and the smaller the length diameter ratio of the pile，the more obvious the radial heterogeneity of the dynamic impedance of the pile. For large-diameter piles，ignoring the radial wave effect of the pile shaft can overestimate the amplitude and frequency of the dynamic impedance at the pile head，which is not conducive to the anti-vibration design of the pile shaft. The proposed three-dimensional fictitious soil pile model not only has better applicability for the vertical vibration of the large-diameter floating pile but also can be used to analyze the dynamic characteristics of the end-bearing pile by ad? justing the parameters of the fictitious soil pile.