As a newly emerged solution for supporting the new generation of offshore wind turbines (OWTs), the pile-bucket foundation has received wide attention. However, little attention has been paid to the grouted connection that connects the monopile and bucket foundation. As the loadtransferring, yet vulnerable component, the fatigue mechanism of the grouted connection and its influence on the cyclic laterally-loaded response of OWT foundation are still not clear. In this study, a sophisticated three-dimensional (3D) finite element (FE) model of the pile-bucket foundation with grouted connection is constructed, which incorporates a hypoplastic clay model and the concrete damage plasticity (CDP) to consider the cyclic load effect on both soil and grout material. A modal analysis is first performed to verify the rationality of the proposed model. Then the influence of cyclic load frequency, load amplitude and stiffener arrangement on the accumulation of pile head displacement, stress distribution and crack development of the grouted connection is systematically analyzed. Results indicate that as load frequency approaches the eigen-frequency, the OWT structure tends to vibrate more intensively, leading to stress concentration and fatigue damage of the grouted material and rapid accumulation of the pile-head displacement. The influence of load amplitude on grout damage seems to be limited in the contact area in the simulated cases. Meanwhile, the installation of stiffeners slightly mitigates the pile head displacement accumulation, but also raises the risk of stress concentration and fatigue damage of the grouted connection. The numerical results reveal the load-transferring function and fatigue damage of the grouted connection, which could provide some reference for an optimized structure and dynamic design for the pile-bucket foundation under cyclic load.