The occurrence of skidding in rolling bearings accelerates surface degradation, diminishes rotational precision, and may result in abnormal vibrations and noise. For a four-contact-point ball bearing (FCPBB), the change in rotating speed will significantly affect the multi-point contact state and internal interactions owing to the centrifugal effect and its special mechanical structure. To investigate skidding behavior, a dynamic model of the FCPBB is constructed by accounting for nonlinear normal contact forces and tangential friction between the balls, raceways, and cage. In addition, the dynamic responses of the ball and cage during the acceleration process are analyzed under the transient influence of the lubricant. The research results indicate that skidding behavior in FCPBBs is attributed to the greater resistance of the components and the smaller traction forces between the balls and the rings. It is worth noting that as the bearing speed increases, the contact conditions evolve, specifically, the two-point contact region contracts while the three-point contact region expands. Variations in the contact state further influence the ball–race interactions and alter the skidding behavior of the bearing. This study can provide a theoretical basis for mitigating or preventing the skidding in FCPBBs during the acceleration phase.