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Optical current transformers, which possess excellent transient characteristics, are able to accurately reflect the full waveform of primary current, and have a wide range of potential applications. The clamp is the sensing unit of the optical current transformer that is mounted directly to the gas-insulated switchgear (GIS) casing and has advantages such as simple structure and ease of maintenance. However, vibration of the casing due to the operation of the GIS circuit breaker has a significant effect on the output of the optical current transformer, and may cause the malfunction of protective relays. This paper proposes the use of damping rubber as the main means of reducing vibration in transformers. A vibration damping system for the clamp-on optical current transformer was designed using the optimal parameters obtained from the modeling and analysis of an anti-impact vibration system. A test system was set up to perform experiments on the designed vibration damping system.