This paper proposes a novel and computationally efficient estimation algorithm for lithium-ion battery state of health (SoH) under the hood of incremental capacity analysis. Concepts of regional capacity and regional voltage are introduced to develop an SoH model against experimental cycling data from four types of batteries. In the obtained models, SoH is a simple linear function of the regional capacity, and the R-square of linear fitting is up to 0.948 for all the considered batteries with properly selected regional voltage. The proposed method without using characteristic parameters directly from incremental capacity curves is insensitive to noise and filtering algorithms, and is effective for common current rates, where rates of up to 1C have been demonstrated. Then, a model-based SoH estimator is designed and shown to be capable of closely matching battery's aging data from NASA, with the error less than 2.5%. Furthermore, such a small scale of error is achieved in the absent of state of charge and impedance which are often used for SOH estimation in available methods.