The self-sensing eddy current damper, which has many advantages such as non-contact, non-mechanical wear and non-additional transducer etc, has been widespread application prospect in vibration control field. This paper presents a mathematical model that describes the inductance change using transformer equivalent circuit when a double-coil eddy current damper is placed next to a conductive plate, while the exciting coil is used as actuator and the detecting is sensor. In addition, the characteristics of the system, which include the relationship of the vibration and mutual inductance, phase, amplitude, eddy current loss power, as well as vibration, average axial force and induced voltage versus time with the different dimension parameters of the coil, excitation frequency and conductive material, are analyzed by simulation using MATLAB software.