This paper presents a smart passive damping system (SPDS) for reducing stay cable vibrations. Stay cables, such as used in cable-stayed bridges, are prone to vibration due to their low inherent damping characteristics. Recently some studies have shown that semiactive control systems using Magnetorheological(MR) dampers can potentially achieve higher performance levels and adaptability with few of the detractions as compared their passive counterparts. However, most semi-active and active control systems that use MR dampers require additional power supplies, controllers, and sensors, adding complexity into the system. The complexity may not be desirable to effectively control many large civil structures. This paper proposes a novel SPDS with MR dampers. The smart passive device includes an electromagnetic induction (EMI) system to power the MR damper and adjust itself to external loadings. Thus, SPDS dose not require any control system. The numerical study considered 12.56m stay cable to evaluate the dynamic performance of the SPDS for mitigating the vibration of stay cables. Moreover, the performances of the smart passive damping system are compared with those of an equivalent linear viscous damper and an MR damper operated in a pssive-mode. Results showed SPDS has competitive performance with others despite of its simplicity.