The electrical insulation design for a superconducting system is important when developing a high-voltage superconducting apparatus as a substitute for a conventional one. In this paper, the degradation characteristics of 2G high temperature superconducting (HTS) wires, with respect to electrical breakdown tests, were studied. It was found that the superconducting materials in 2G HTS wires can be damaged in electrical breakdown, and the damaged structure of 2G HTS wires results in the degradation of the Ic and index number. As a result, it was found that the degradation characteristics of the 2G HTS wires were affected by the stabilizer material and applied breakdown voltage. Thus, the hardness and electrical conductivity of a stabilizer material can be considered as design parameters in developing a high-voltage superconducting coil. Finally, the cross-sectional views of 2G HTS wires were presented using a scanning electron microscope.