Using an equivalent circuit model to characterize the constant-current part of a charging/discharging profile, a model is developed to estimate the state-of-health of lithium ion batteries. The model is an incremental capacity analysis-based model, which applies a capacity model to define the dependence of the state of charge on the open circuit voltage as the battery ages. It can be learning-free, with the parameters subject to certain constraints, and is able to give efficient and reliable estimates of the state-of-health for various lithium ion batteries at any aging status. When applied to a fresh LiFePO4 cell, the state-of-health estimated by this model (learning-unrequired or learning-required) shows a close correspondence to the available measured data, with an absolute difference of 0.31% or 0.12% at most, even for significant temperature fluctuation. In addition, NASA battery datasets are employed to demonstrate the versatility and applicability of the model to different chemistries and cell designs. (C) 2019 Elsevier Ltd. All rights reserved.