Based on the Biot dynamic consolidation equation and the Kelvin model, the vertical vibration characteristics of the incompletely bonded pipe pile in saturated soil are investigated by considering the three dimensional effect of soil and the relative slip between the soil plug and pipe pile. Firstly, by introducing the potential functions and combining with the initial conditions and boundary conditions of the pile surrounding soil and soil plug, the vertical vibration solutions of the pile surrounding soil and soil plug are obtained by the Laplace transform method, Helmholtz decomposition method and separation variable method, respectively. Then, combining with the coupling conditions of pile-soil system, the complex stiffness, the frequency domain solution of the velocity and the semi-analytical solution of the velocity in the time domain of pipe pile top are obtained. Next, the degenerate solutions of this paper are compared with the corresponding existing solution to verify the rationality of the solution of this paper. Similarly, a parametric sensitivity analysis of the Kelvin model is conducted to preliminarily obtain the suitable values of the parameters of Kelvin model. Finally, the influence of the length of pipe pile, the permeability coefficient, porosity, shear modulus and viscous damping coefficient of soil plug on the vertical vibration characteristics of the incompletely bonded pipe pile in saturated soil are studied. The results show that, the shorter length of pipe pile leads to more obvious influence of the degree of bond between the soil plug and pipe pile on the vertical vibration characteristics of pipe pile in the saturated soil. The porosity and viscous damping coefficient of the soil plug have obvious influence on the vertical vibration characteristics of incompletely bonded pipe pile in saturated soil, and the influence of shear modulus and permeability coefficient of soil plug are too small to be neglected.