A superconducting generator is now under intensive study as one application of superconductivity, since it has some advantages over a conventional generator. It has conductive dampers for damping vibration and for shielding field change in time. This shielding effect prevents AC joule loss from generating in the superconductors. Quantitative evaluation of the effects requires 3-D analysis of eddy currents induced in the damper. Among various methods of 3-D eddy current analysis, current vector potential method (T-method) would be efficient in terms of numerical calculation, especially when thin plate approximation holds. In this study a 3-D eddy current code based on this method has been developed and applied to eddy current analysis of the damper in a superconduting generator. Obtained results have some difference compared with results from 2-D analysis and show influences of the damper edges. Especially, decrease in shielding effect near the edge would be important for the damper design. This method of 3-D eddy current analysis would be useful for magnetomechanical design of thin conductive structures.