For reliable operation of lithium-ion battery (LiB) in hybrid electric and electric vehicles, it is necessary to estimate the state of health (SOH) as well as the state of charge (SOC). The SOH is a measurement that reflects the general condition of a LiB compared with a fresh battery. Since the cell capacity deteriorates fairly linearly with cycle life, the remaining cycle life is often used as a measure of the SOH. However, unlike the SOC, there is no absolute definition of the SOH so far because battery performances can be differently defined according to manufacturer''s own set of rules. Most of existing methods are based on the measurement of internal resistance or impedance from 0.001 to 2,500 Hz. It is important to note that those parameters are significantly dependent upon temperature and C-rate of a LiB. This is a reason why the good estimation of SOH is the change of battery capacity reflects on the electrochemical the change very difficult. The purpose of the work in this thesis is to investigate how of battery capacity reflects on the electrochemical impedance spectroscopy. Based on the result, a new SOH estimation method is proposed. We here define the SOH as the ratio of current capacity to initial cell capacity. To cover the problems that impedance of a cell varies with the changes of temperature and C-rate, the multiple equivalent models of LiB in [1] have been used. Those model set are identified in two separate linear regions of the open circuit voltage and are obtained at every operating point corresponding to a pair of temperature and C-rate, where each operating point is generated by properly dividing them within a given range. For this analysis, we derive a Thevenin equivalent circuit model of LiB from the model set. It turns out that the Thevenin''s equivalent impedance comes to a transfer function whose coefficients include cell capacity. Then we investigate the relationship between the change of capacity and the frequency responses of cell impedance. As a result, the reduction of cell capacity dominantly affects the phase of the impedance over the frequency range lower than 0.03 Hz while hardly makes its magnitude be changed. This property leads to a new method for the SOH estimation. Only if phases of cell impedance at some frequencies from 0.01 to 0.03 Hz are measured, the corresponding SOH can be determined from the phase vs. SOH curves. In addition, we investigate how the cell impedance is affected according to the level of SOC and temperature. The proposed method is demonstrated through simulations that are performed for a Bellcore LiB model of 40 Ah.