An offshore wind power AC grid-connected system has a different structure and operational characteristics from an onshore system. The dynamic var compensation device (SVG) is usually located at onshore centralized control station instead of the wind farm outlet, and generally operates in an inductive state compensating the charging reactive power of the AC cable. In this case, it is necessary to study the impact of the SVG on the oscillation characteristics of the system. In this paper, a practical direct-drive offshore wind power AC grid-connected system is selected as a case study. Based on eigenvalue analysis, some comparative cases are constructed to study the impact of SVG capacity, operational region as well as its control on the stability of the dominant oscillation mode. It is found that the stability of the dominant subsynchronous oscillation mode is significantly weaker when SVG is working in an inductive state compared with SVG working in a capacitive state. In addition, current inner control and power outer control parameters of the SVG could lead to instability in the dominant oscillation mode. The control parameter design of a SVG should be adapted to system operation and coordinated with the control of the wind turbine generator for stable operation. A detailed electromagnetic transient simulation based on PSCAD/EMTDC validates the results. The study would be beneficial to understanding the characteristics of an offshore wind farm AC grid-connected system as well as guiding system planning and optimal operation. This work is supported by the Research and Development Plan in Key Areas of Guangdong Province (No. 2021B0101230004).