Considering the three-dimensional effect of the pile and the interaction of the pile, seawater and seabed, a theoretical model is developed to investigate the dynamic response of the monopile embedded in viscoelastic ground under vertical load. The pile is simplified as a three-dimensional axisymmetric homogeneous elastic medium, and its governing equation is established. The seawater is assumed to be an inviscid compressible fluid, while the seabed is regarded as a viscoelastic medium, and their governing equations are constructed respectively. Then, the variable separation method is used to solve the governing equations, and the analytical solutions for the dynamic response of the pile are obtained by combining the boundary conditions of the pile, seawater and seabed. By comparing with the degenerated one-dimensional pile-soil interaction model and the pile-water-soil finite element model, the correctness of the model in this paper is verified. Compared with the one-dimensional model, the results show that the three-dimensional pile can more accurately reflect the interaction between the pile, seawater and seabed, revealing a more complex wave propagation mechanism. For a large-diameter pile under vertical load, the traditional one-dimensional pile model would overestimate the peak velocity of the reflected wave at the pile top due to neglecting the pressure and radiation damping of seawater and seabed.