In the power system, the On-load Tap-changer (OLTC) plays an essential role in maintaining voltage stability and increasing the power grid's scheduling flexibility. Despite the increasing influence of on-load tap-changers on transformer faults, the study of partial discharge processes caused by air bubbles in OLTC is still limited. The production of a small number of bubbles during normal operation can lead to partial discharge in high field intensity areas within the tap-changer, posing significant security risks to power system operations. Studying the dynamic behavior of bubbles in tap-changers and how they interact with insulating oil is therefore crucial. Based on the real structure of OLTC, we build a mathematical model of fluid flow and a physical model of internal electric field distribution in this study. We discuss the influence of bubbles within the oil channel on electric field distribution within the tap-changer as well as examine bubble deformation and changes in maximum field strength under different influencing factors.