The wind-induced vibration of stay cables of cable-stayed bridges, which includes rain-wind-induced vibration (RWIV) and dry galloping (DG), has been studied for a considerable amount of time. In general, mechanical dampers or surface modification are applied to suppress the vibration. In particular, several types of surface-modification cable, including indentation, longitudinally parallel protuberance, helical fillet, and U-shaped grooving, have been developed. Recently, a new type of aerodynamically stable cable with spiral protuberances was developed. It was confirmed that the cable has a low drag force coefficient, like an indented cable, and that it prevented the formation of water rivulets on the cable surface. In this study, the stability for RWIV of this cable was investigated with various flow angles and protuberance dimensions in a wind-tunnel test. It was found that the spiral protuberance cable is aerodynamically stable against both RWIV and DG for all test wind angles. The effects of the protuberance dimensions were also clarified.