Based on saturated porous media theory, the vertical vibration of large diameter piles with variable sections in homogeneous saturated soil is studied. Firstly, according to the dynamic control equation of saturated soil, the complex stiffness is obtained. The bottom of pile adopts viscoelastic support, Then, the pile body is divided according to variable sections. The dynamic equation of large diameter piles is established by Rayleigh-Love rod model which can consider the transversal inertia effect.Combining the initial condition, boundary condition and continuous condition, the impedance recurrence method is used to solve the coupling equation of large diameter pile-soil dynamic equation with variable sections. The analytical solution of pile top in frequency domain is obtained. The semi-analytical solution of pile top velocity in time domain is obtained by convolution theorem and inverse Fourier transform. Then, the finite element model is established by ANSYS/LS-DYNA, the numerical and theoretical solutions are compared and analyzed under various working conditions. The correctness of the theoretical calculation model is verified by numerical solutions.