An extensive numerical investigation on the magnetorheological (MR) damper-based smart passive control system for mitigating vibration of stay cables under wind loads has been conducted. The smart passive system is incorporated with an electromagnetic induction (EMI) device for reducing complexity of the conventional MR damper based semi-active control system by eliminating an external power supply part and a feedback control part (i.e., sensors and controller). In this study, the control performance of the smart passive system has been evaluated by using a cable structure model extracted from a full-scale long stay cable with high tension. Numerical simulation results of the proposed smart damping system are compared with those of the passive and semi-active control systems employing MR dampers. It is demonstrated from the results that the control performance of the smart passive control system is better than those of the passive control cases and comparable to those of the semi-active control systems in the forced vibration analysis as well as the free vibration analysis, even though there is no external power source in the smart passive system.